How does transubstantiation account for the amount of Christ's body eaten over the last 2000 years?

Great question! I will attempt to explain this from my Catholic roots, as well as my current non-denominational standpoint - both of which were similar, though I hold that not every church, even Catholic, is 100% the same.

We take Jesus' divinity into account. He is the Lord God's only Son, the Lord God in the Flesh, and the Word/Truth - He was present at the foundation of the world, and the world was created through Him (as the Word, and God).

As the Lord God, and even as the Son, many times we see that He does not change - then, now, and forever! In church I was taught to apply this to the transubstantiation.

Even though we are literally eating and drinking of the Lord, His never-changing status as the Son and Lord prevents Him from change,and thus He can never run out of Himself (apologies if that grammar appears odd, it's the best way I could word it).

For us to teach that His body "runs out" would be applying a finite attribute to the Lord and Son, who is by a Biblical standpoint clearly infinite in all attributes.

This article for an online "spiritual seekers" magazine by a Fr. Joe Scott uses the following excerpt as it pertains to Catholicism:

In Aristotle’s philosophy, things can share the same nature even when they differ in some specifics. For example, a brown wooden rocking chair and a red overstuffed sofa are both recognizable as chairs, even though they look very different from one another. What makes them both “a chair” is their substance, while the size, color, shape, texture and other things that differentiate them are called “accidents.”

The teaching of transubstantiation, as summarized by St. Thomas Aquinas, the great theologian of the 13th century, was that “the whole substance of the bread is changed into the whole substance of Christ’s body, and the whole substance of the wine into the whole substance of Christ’s blood.” The accidents–color, texture, shape, and so on–remain those of bread and wine. When you eat and drink, for example, the host does not bleed. You taste bread and wine. But the substance, the very nature of this reality is now Christ’s body and blood.

I think that there are 2 questions being answered. One is a question of the real presence of Christ in the Eucharist.

The other question is, if Christ is really present in the Eucharist would that mean he has infinite mass ? This second question calls up images of an almost infinite sized human being which seems to make the real presence of Christ in the Eucharist illogical. This second question is more of a question of logic than of Church teaching. It seems to imply that the particular Church teaching has illogical conclusions.

The above answers are all very good. I would like to try to more specifically address the second question about infinite mass and images of infinitely huge beings.

First, when the Eucharist is consumed and it breaks down into it's constituent parts, it ceases being the body and blood of Christ (Catechism of the Catholic Church 1377 "The Eucharistic presence of Christ begins at the moment of the consecration and endures as long as the Eucharistic species subsist.") So, you could not take the sum a total of Eucharist's over a period of time.

Natural bodies, as we are commonly familiar with them, are constantly changing in the material that constitutes them. For example, if you weigh 150 lbs., then over a period of a month the material that had been or presently constitutes your body would weigh more than 150 lbs. Your weight and height can remain the same over that period, but the material that constitutes you can change. So, you are not the sum total of the material that has been you over time. Even if your height and weight remained the same for 10 years, the sum total of the material that had been you could be much, much larger.

Second, it is the body and blood of the risen Christ that is consumed (Catechism of the Catholic Church 1373 “Christ Jesus, who died, yes, who was raised from the dead, who is at the right hand of God, who indeed intercedes for us,” is present in many ways to his Church: in his word, in his Church’s prayer, “where two or three are gathered in my name,” in the poor, the sick, and the imprisoned, in the sacraments of which he is the author, in the sacrifice of the Mass, and in the person of the minister. But “he is present... most especially in the Eucharistic species.)

That it is the risen body and blood of Christ along with the fact that Christ is God means that the body and blood of Christ are not exactly the same as the human bodies we are more familiar with. Just as God (Christ) can be at different places at the same time, so His risen body and blood can be at different places at the same time (see CCC 1374 which may be helpful in this regard). Other answers already provided here address the question of the real presence.

Catechism of the Catholic Church 1374 "The mode of Christ’s presence under the Eucharistic species is unique. It raises the Eucharist above all the sacraments as 'the perfection of the spiritual life and the end to which all the sacraments tend.' In the most blessed sacrament of the Eucharist 'the body and blood, together with the soul and divinity, of our Lord Jesus Christ and, therefore, the whole Christ is truly, really, and substantially contained.' 'This presence is called ‘real’—by which is not intended to exclude the other types of presence as if they could not be ‘real’ too, but because it is presence in the fullest sense: that is to say, it is a substantial presence by which Christ, God and man, makes himself wholly and entirely present.'"

The question presumes transubstantiation is a belief system and that we ought to understand it materially and literalistically. Yet this misses completely what it is and what it means to explaining what Catholics mean when they use this term. If it meant literalistically Christ was present on the altar, then the question would have validity, but this is not what it means, so the subsequent question fails to address reality but rather an inaccurate understanding much like a strawman argument. There isn't technically mass to Jesus sacramental presence since it is only the substance that is changed, the accidents remain as they were, yet the reception of the accidents gives one the substance of Christ's Body & Blood, changing the recipient into Jesus' image from glory to glory. Hence we read in the Catholic Catechism (note the Diadache dates as early as 60 to about 150AD and St. Ignatius of Antioch was martyred between 107-115AD, most likely at the earliest date):

1331 Holy Communion, because by this sacrament we unite ourselves to Christ, who makes us sharers in his Body and Blood to form a single body. [Cf. 1 Cor 10: 16-17] We also call it: the holy things (ta hagia; sancta) [Apostolic Constitutions 8, 13,12 PG 1,1108; Didache 9, 5; 10:6: SCh: 248,176- 178] - the first meaning of the phrase “communion of saints” in the Apostles' Creed - the bread of angels, bread from heaven, medicine of immortality, [St. Ignatius of Antioch, Ad Eph. 20, 2 SCh 10, 76] viaticum....

This is an idea taken from philosophy using the ideas of substance, or reality, and accidents, or material appearance. So for example, when the bread is consecrated, the reality (substance) of the bread is changed into the body of Christ and the material appearance (accidents) are not changed, so the bread still looks, smells and tastes like bread and the same for the wine, yet the substance of the bread and wine are changed. In this, Christ offers us his body and blood for the food of eternal life just as Jesus said not only in John 6, "he who eats my body and drinks my blood has eternal life, and I will raise him up on the last day", but also in the synoptic accounts of the last supper where Jesus clearly states "this is my body broken for you" and likewise for the wine. Reference the Catholic Catechism

on the Institution narratives:

1323 “At the Last Supper, on the night he was betrayed, our Savior instituted the Eucharistic sacrifice of his Body and Blood. This he did in order to perpetuate the sacrifice of the cross throughout the ages until he should come again, and so to entrust to his beloved Spouse, the Church, a memorial of his death and resurrection: a sacrament of love, a sign of unity, a bond of charity, a Paschal banquet 'in which Christ is consumed, the mind is filled with grace, and a pledge of future glory is given to us.'“ [Sacrosanctum Concilium 47 (Constitution on the Sacred Liturgy)]

and on John 6

1336 The first announcement of the Eucharist divided the disciples, just as the announcement of the Passion scandalized them: “This is a hard saying; who can listen to it?” [Jn 6:60] The Eucharist and the Cross are stumbling blocks. It is the same mystery and it never ceases to be an occasion of division. “Will you also go away?”: [Jn 6:67] The Lord's question echoes through the ages, as a loving invitation to discover that only he has “the words of eternal life” [In 6:68] and that to receive in faith the gift of his Eucharist is to receive the Lord himself.

About which St. Irenaeus of the second century (130-202AD), wrote

1327 ... “Our way of thinking is attuned to the Eucharist, and the Eucharist in turn confirms our way of thinking.” [Adv. haeres. 4, 18, 5: PG 7/l, 1028 (Against Heresies)]

This is why the Church states the following about the Eucharistic species (transubstantiated bread and wine) in the Council of Trent, Chapter 1, first sentence:

In the first place, the holy Synod teaches, and openly and simply professes, that, in the august sacrament of the holy Eucharist, after the consecration of the bread and wine, our Lord Jesus Christ, true God and man, is truly, really, and substantially contained under the species of those sensible things

There are several churches which use the idea of transubstantiation; but the Eastern churches (Eastern Orthodox, Oriental Orthodox, and Assyrian Church of the East) share a similar view on how it works. I'll therefore split my discussion into two parts, the "Eastern" and "Western" views.

Eastern View

The Eastern churches have occasionally used the term "transubstantiation"; sometimes (being Greek-speaking in origin) they would use the Greek-derived equivalent "metousiosis". They don't get very specific about how transubstantiation works technically. The Longer Orthodox Catechism (articles 339 - 340) states:

The bread and wine are changed, or transubstantiated, into the very Body of Christ, and into the very Blood of Christ. ...
In the exposition of the faith by the Eastern Patriarchs, it is said that the word transubstantiation is not to be taken to define the manner in which the bread and wine are changed into the Body and Blood of the Lord; for this none can understand but God; but only thus much is signified, that the bread truly, really, and substantially becomes the very true Body of the Lord, and the wine the very Blood of the Lord.

In other words, they're just saying they believe that the bread and wine "become" the Body and Blood of Christ, but they don't know (and really don't care) how; it is a mystery. The Eastern churches in general don't do as much philosophical speculation in their theology as the Western ones historically have; they have an entirely different approach. Certainly, they are aware and believe that the bread doesn't become body parts in some sort of literal sense. Thus, they're not concerned with the possibility that the consecrated Hosts become parts of Christ's body and add to his weight.

The Western View

The most systematic approach we have to an answer here is probably through the work of Thomas Aquinas, particularly his treatise Summa Theologica ("A Summary of Theology"). Unfortunately, it's very difficult to understand what Aquinas says about it simply by reading the book, without knowing a good bit of medieval philosophy, particularly medieval interpretation of Aristotelian philosophy. Aquinas' take on whether Christ's weight (or other aspects of his body) is really present in the consecrated host is this:

As stated above, any part of Christ is in this sacrament in two ways: in one way, by the power of the sacrament; in another, from real concomitance. By the power of the sacrament the dimensive quantity of Christ's body is not in this sacrament; for, by the power of the sacrament that is present in this sacrament, whereat the conversion is terminated. But the conversion which takes place in this sacrament is terminated directly at the substance of Christ's body, and not at its dimensions; which is evident from the fact that the dimensive quantity of the bread remains after the consecration, while only the substance of the bread passes away.

Nevertheless, since the substance of Christ's body is not really deprived of its dimensive quantity and its other accidents, hence it comes that by reason of real concomitance the whole dimensive quantity of Christ's body and all its other accidents are in this sacrament.

(Third Part, Question 76, Article 4)

This, like a very dry Host, is rather hard to swallow all at once. Essentially what it means is this: The weight of a physical entity is one of its accidents, one of the things that just happens to be true of it in particular, but doesn't change what kind of thing it is. (So my weight could change without changing whether I'm human or not.) Since transubstantiation changes the substance of the bread and wine, but not their accidents, transubstantiation does not directly give the bread and wine the weight, or height, or eye color, or what-have-you, of Jesus.

However, there's a surprise waiting: the doctrine of concomitance. This simply says that nothing about Christ, including body, blood, and what-have-you, is really separable from anything else about Him, so that if He's present in some sense, he's present in all senses. Thus, through the "real concomitance" approach, his weight is there. The weight of the Host, however, is a different accident—it's "attached to" the other accidents of the bread, which remain the same, and so it doesn't alter the weight of Christ.

Clear as mud? I thought so. Let me know what I can do to clarify it.