Biblically, there are three principal categories of sin.
- Lust of the flesh
- Lust of the eyes
- Pride of life
For all that is in the world, the lust of the flesh, and the lust of
the eyes, and the pride of life, is not of the Father, but is of the
world. (1 John 2:16, KJV)
It was upon these three categories of sin that Jesus was tempted in the wilderness.
Lust of the flesh includes the fleshly appetites of every sort, whether of indulging oneself in areas of eating, sexuality/sensuality, sleep/laziness, drunkenness, or any other activity that appeals to physical comforts and pleasures. All of these sins are part of the "lust of the flesh" category, and it is often true that one who is weak on one of these may experience weakness in another sin of the same sort.
As an illustration, consider cheating in school: studies have shown that those who cheat in school are more likely to cheat in other areas of life in the future, including sexually, on their taxes, etc. The basic weakness carries over to these other areas, and the cheater who believes he or she will not get caught--thinking it is a sin which can be hidden--will be more likely to "cheat" in other areas where this same false belief may be held.
Many who indulge their appetites for food will also be weak in the area of their sexual appetites.
The word "immoral" itself, while often used nowadays with a sexual application, does not strictly refer only to sins of a sexual nature. It implies any sin which violates the standard of principle, particular with respect to those standards commonly held by society. Thus, overeating is a potential sin of "immoral" category: consider issues with obesity, anorexia, and bulimia, and how these appear to society in general.
Yet the Greek word translated here as "sexual immorality" is actually "πορνεύων/porneuon"--of the same root from which stems our modern "pornography." The KJV translates it as "fornication"--a word with clear sexual connotations.
Flee fornication. Every sin that a man doeth is without the body; but
he that committeth fornication sinneth against his own body. (1
Corinthians 6:18, KJV)
However, it should be remembered that this word also addresses spiritual forms of adultery, e.g. idolatry; and in many of the pagan, idolatrous or hedonistic practices, food festivals featured prominently. All of these gluttonous and lustful indulgences are denounced in Paul's words.
Conclusion
There is certainly a physical connection between gluttony and lust--both being appetites of the flesh; weakness in the first area will create greater temptation in the latter, just as drinking alcohol often precedes the loss of one's virginity. But there is a spiritual application as well: indulgence to excess in even the necessaries of life will weaken our stance against spiritual adultery--even the food itself can become an idol, and cause us to be led astray, committing "fornication" against God.