What is the scriptural basis for gluttony being a sin?

Vices (Capital / Deadly Sins) are opposed to Virtues

Soundbyte answer (scripture)

Sirach 18:33 Become not a glutton and a winebibber with nothing in your purse.

Scripture supporting the virtue of Temperance, which is Gluttony's opposite:

• Esther 1:7 Esther 1:8 ; Proverbs 23:1-3 ; 25:16 ; Daniel 1:8 Daniel 1:12-16 ; Romans 13:14 ; 1 Corinthians 9:25 1 Corinthians 9:27 ; Philippians 4:5 ; 1 Thessalonians 5:6-8 ; 1 Timothy 3:2 1 Timothy 3:3 1 Timothy 3:8 ; Titus 1:7 Titus 1:8 ; Titus 2:2 Titus 2:3 Titus 2:12 ; 2 Peter 1:5 2 Peter 1:6; Sirach 37: 28-30

Reasoning based on scripture for why a vice (for example gluttony) is a sin.

Most of the scriptural support for that position relates to temperance (ample citations in both OT and NT). Since gluttony is in opposition to temperance, and temperance is a virtue, and temperance is amply cited in scripture as how one should behave, then gluttony is framed as a sin, though its character as a sin becomes a matter of degree.

The Definition of Sin

CCC 1849 Sin is an offense against reason, truth, and right conscience; it is failure in genuine love for God and neighbor caused by a perverse attachment to certain goods. It wounds the nature of man and injures human solidarity. It has been defined as "an utterance, a deed, or a desire contrary to the eternal law."(Saint Augustine).

The four cardinal virtues taught from the Roman Catholic perspective are: prudence, justice, fortitude, and temperance. (CCC 1805; Wisdom 8:7) Scripture supports Temperance as a virtue. To directly oppose virtue is to pursue or to commit (or to be predisposed to commit) sin.

• Note: gluttony may be classified a venial sin, rather than as a mortal sin. It's being "deadly" or "capital" is not negated by that classification. Like other venial sin, it predisposes one to sin in general. In due course, this is believed to lead to more serious (mortal) sin.

  1855 Mortal sin destroys charity in the heart of man by a grave violation of God's law; it turns man away from God, who is his ultimate end and his beatitude, by preferring an inferior good to him. Venial sin allows charity to subsist, even though it offends and wounds it.

  To put that in modern jargon, some sins (mortal) put you in the waiting line to get into Hell. Without an explicit turning back to God, repentance, baking or broiling is in the cards. Lesser sin (venial) puts you on the highway to hell, but there is more time or hope for a detour (through Christ, reconciliation, repentance, penance, prayer, etc) to turn around. (From the older meaning of repentance, which is "to turn again, toward God" -- the connotation being that you turned away from God through sin in the first place).

  Confusion in terms. Mortal sin ("sin unto death") is the condition or state wherein life {eternal life, life with God} is either voided, at risk, or in some way a first class ticket to damnation. What is now referred to as capital sin (to avoid confusion, I suppose, from deadly sin meaning mortal sin) may not necessarily be deadly (mortal) but it also may be. (For example, another vice, lust can be or can lead to mortal sin per Jesus' admonition about those who lust after another's wife already being adulterers ...)

  A variety of scripture on avoiding sin (to whatever degree) is folded into the tradition of classifying the seven deadly sins / seven capital sins. (This answer is confined to the Catholic perspective. @DickHarfield has provided some historical context on the origins of this belief: the Catechism cites the same tradition).

What are vices? (Capital / Deadly sins)

V. The Proliferation of Sin
CCC 1865 Sin creates a proclivity to sin; it engenders vice by repetition of the same acts. This results in perverse inclinations which cloud conscience and corrupt the concrete judgment of good and evil. Thus sin tends to reproduce itself and reinforce itself ...
CCC 1866 Vices can be classified according to the virtues they oppose, or also be linked to the capital sins which Christian experience has distinguished, following St. John Cassian and St. Gregory the Great. They are called "capital" because they engender other sins, other vices. They are pride, avarice, envy, wrath, lust, gluttony, and sloth or acedia.

Gluttony as a deadly sin (Capital sin)

The vice (capital sin/deadly sin) of gluttony is opposed to the virtue of temperance. It is considered a capital sin because it leads to sin and near occasions of sin. Why? Focus in earthly/fleshy/material things, things of the world, rather than focus on God. (1 John 2:6-17, per @Marc's citation).

What is temperance?

CCC 1809 Temperance is the moral virtue that moderates the attraction of pleasures and provides balance in the use of created goods. It ensures the will's mastery over instincts and keeps desires within the limits of what is honorable. The temperate person directs the sensitive appetites toward what is good and maintains a healthy discretion: "Do not follow your inclination and strength, walking according to the desires of your heart." (Sirach 5:12) Temperance is praised in the Old Testament: "Do not follow your base desires, but restrain your appetites." (Sirach 18:30) In the New Testament it is called "moderation" or "sobriety." We ought "to live sober, upright, and godly lives in this world. (Titus 2:12)"

Given the virtue presented, avoidance of the opposed vice follows. When temperance is not pursued, sin will follow.

An example from the book of Sirach.

Sirach 18:30
27 A wise man is circumspect in all things; when sin is rife he keeps himself from wrongdoing.
28 Any learned man should make wisdom known, and he who attains to her should declare her praise;
29 Those trained in her words must show their wisdom, dispensing sound proverbs like life-giving waters.
30 Go not after your lusts, but keep your desires in check.
31 If you satisfy your lustful appetites they will make you the sport of your enemies.
32 Have no joy in the pleasures of a moment which bring on poverty redoubled;
33 Become not a glutton and a winebibber with nothing in your purse.

An example from the epistle to Titus 2:11-14

11 For the grace of God has appeared, saving all 12 and training us to reject godless ways and worldly desires and to live temperately, justly, and devoutly in this age, 13 as we await the blessed hope, the appearance* of the glory of the great God and of our savior Jesus Christ, 14 who gave himself for us to deliver us from all lawlessness and to cleanse for himself a people as his own, eager to do what is good.

(Lawlessness implies sin / vice)

A "deadly" sin may be, or may lead to, mortal sin. It's a matter of degree.

Gluttony is at least (as a vice) a venial sin. Self indulgence is believed to lead to other sin due to focus on the flesh/world, away from God. It can go from deadly to mortal depending on whether a person indulges themselves in it. It remains capital/deadly in the sense that it leads us in the wrong direction, which ultimately (if left uncorrected) can only lead to one place: damnation.

A crude physical analogy:
There are varying degrees of physical danger (analog for sin) via ingestion.

1. Heavy drinking/alcoholism (venial) can lead to death, but there is time, for all the wrong that it does, to reverse the trend. It may also lead to drunk driving and either killing one's self, or killing someone else. (mortal sin).
2. Drinking hemlock (mortal) leads straight to death.

(note l) In love, we pray (1 Jn 5:16–17) for those who are in sin, but not in deadly sin (literally, “sin unto death”), probably referring to apostasy or activities brought on under the antichrist;