Why did the medieval church become involved with marriage?

The case of King Lothair II against Pope Nicholas I is what really interested the Church in judging what constitutes a valid marriage.

A particularly striking instance occurred in the dispute over the marriage of King Lothair II and Theutberga, which involved Pope Nicholas I in the years 860-869 and caught much attention in the Church and in the world. The question, which occupied several synods, was whether the king could separate from his legitimate wife, Theutberga, for lack of offspring in order to marry his former concubine Waldrada, with whom he had lived earlier in a so-called Friedelehe (love marriage) and with whom he already had had a son, Hugo, along with several daughters. The disputes became so fierce that at one point a Frankish army even invaded Rome and threatened the Pope.

It ended up being that, due to immense political pressure on the Pope to support King Lothair, "it cannot but be called logical when [Pope] Nicholas I called the attempt to contract a Muntehe [dowered marriage] with Waldrada a grave sacrilege."

Also:

Against the backdrop of the matrimonial scandals of King Henry VIII and the double marriage of Philip of Hesse, which was “permitted” by Luther, the Council [of Trent Session 24, 11 Nov. 1563,] in canon 2, De matrimonio [On Matrimony], defined explicitly: “If anyone says that it is lawful for Christians to have several wives at the same time and that this is not forbidden by divine law, let him be anathema.”

Walter Cardinal Brandmüller, “5. Unity and Indissolubility of Marriage: From the Middle Ages to the Council of Trent,” in Remaining in the Truth of Christ: Marriage and Communion in the Catholic Church, ed. Robert Dodaro (Ignatius Press, 2014).

This question is somewhat misleading because it makes no distinction between a Sacrament that does not necessarily require formal distribution by the Church (ex: Marriage, Baptism and Penance) and a Sacrament that does require formal distribution (Communion), as organized in ritual. 'Sacrament' here is being used not simply as a term thus for Church rituals, but rather for special unions and contracts in humanity that the Church has authority over in terms of distributive power as of a formal cause or proper knowledge regarding the nature of the union. As to which way the Church delegates this authority, such depends on the Sacrament itself and the understanding of the Church at the time (I would argue that marriage has been a sort of 'unofficial' Sacrament all throughout the early Church history, for obviously the Church exercised proper knowledge in the dealings of union).

In certain Sacraments, the grace achieved can in fact be achieved through a means that is not yet formally distributed by the clergy (the only exception being Communion). Even Baptism, though perhaps requiring a formal definition of its nature, can be distributed by those outside of the Church. This is because the nature of the Sacraments (again, besides Communion) do not formally rely on the Church for distribution. But this is not to say that the ones carrying out these Sacraments do not rely upon the infallibility of the Church to clarify what the purpose of these Sacraments are and the nature by which they are performed. Indeed, such a shared understanding is a necessity for the perfect practice of any such Sacrament. 'Marriage' itself always had to be an act of peace for those who considered themselves Christians, despite the Church's non-direct involvement in such a consensual agreement. And as an act of peace, the primary authority in understanding its nature was the Church, even if it was not the formal cause of the marriage contract. It is not as though there was a time in which the Church did not support a pure and God-centered marriage. For example, consider the verse Hebrews 13:4:

Let marriage be had in honor among all, and let the bed be undefiled: for fornicators and adulterers God will judge.

So to the question:

So, does that mean that before the Middle Ages, the Western Christian church did not really care about marriage?

The answer is rather plainly 'no'. The Church certainly has always been clear on the call of Christians to purity and the continuing moral theory that sexual impurity (such as h*m*sexual acts, adultery, fornication, etc) are all detrimental precisely because such acts are contrary to natural law and as such destruct both the opportunity of utmost purity in celibacy and likewise purity in the intended marriage between a man and a woman.

As to why the Church formally delegated itself as the distributor of marriage in the Middle Ages, and formally stated Marriage as a Sacrament in the same way Communion and Baptism were considered Sacraments, it is largely because of St. Augustine's resurgent influence in the Middle Ages. But before further explanation, it is important here again to note that it is not as though the Church did not already intervene in the marriage process. As far back as Tertullian we find examples of witnesses asking for clergy members to marry them. In most cases in which there were disagreements regarding the nature of the marriage, the issue was resolved in ecclesiastical courts. In certain Orthodox traditions ranging back to the fourth century, it was customary for a priest to be a witness of a marriage. There are many other examples of a closeness of the Church to both the understanding of marriage and the practice of marriage. So the idea that the Middle Ages simply engendered some new and unexpected invasion of the Church into personal life (which is often the stance taken by overly zealous historians) is rather ridiculous.

As stated, the purpose for which the Church formally declared itself as the distributor of marriage is largely due to the increasing ideological influence from St. Augustine and other Church Fathers who looked favorably upon marriage as a higher form of contract than perhaps previously thought in and by the Church (St. Augustine himself using 'Sacrament' to describe marriage). It is also due to several heretical ideologies that formed in the Middle Ages regarding the nature of Sacraments and other unions, a few examples being Catharism and Waldensianism. Being influenced by St. Augustine, and hoping to counteract the heresies at the time, the Church ensured the protection of the union of marriage in its own faculty and language by making it a practice formally delegated to the clergy. Thus is it that the first 'official' decleration of marriage as a Sacrament was made in the 1184 Council of Verona, specifically in response to the Cathars.

Before the Middle Ages, the Western Christian church did not really care about marriage?

For most of Church history, matrimony had been celebrated without clergy and was done according to local customs. The first available written detailed account of a Christian wedding in the West dates only from the 9th century and appears to be identical to the old nuptial service of Ancient Rome. However, early witnesses to the practice of intervention by the clergy in the marriage of early Christians include Tertullian, who speaks of Christians "requesting marriage" from them, and Ignatius of Antioch, who said Christians should form their union with the approval of the bishop - although the absence of clergy placed no bar, and there is no suggestion that Ignatius' recommendation was widely adopted.

Over a period of centuries, the Catholic Church began to take control of the wedding and began to provide the sacrament of marriage. Taking the lead of Augustine (354-430), the Church developed the sacramental understanding of matrimony. James A. Brundage says, in Law, Sex, and Christian Society in Medieval Europe page 236, Gratian [the 12th-century "Father of canon law"] held that it was consummation that turned marriage into a sacrament, thereby making it indissoluble.

In time, the Church regarded a clandestine marriage as being subject to annulment. The Catholic Church forbade clandestine marriage at the Fourth Lateran Council (1215), which required all marriages to be announced in a church by a priest. Prior to that time, an unwitnessed exchange of marriage vows was deplored but still valid. The decree was enforced only in those regions where it could be proclaimed in the vernacular.

The Council of Trent (1545–1563) introduced more specific requirements, ruling that in the future a marriage would be valid only if witnessed by the pastor of the parish or the local ordinary (i.e., the bishop of the diocese), or by the delegate of one of said witnesses, the marriage being invalid otherwise, even if witnessed by a Catholic priest.