We do not look at a fat priest and judge him. That is up to his bishop. Gluttony is a private sin best left to his father confessor. Homosexuality is a public sin demonstrating that a person has fallen away from the faith.
It is the same to say of a homosexual priest who does not flaunt his sin. It is left to the bishop.
Gluttony is a form of worldliness and so is the desire for wealth.
Not much difference between gluttony and homosexuality.
Proverbs 23:2
And put a knife to your throat If you are a man of great appetite.
Deuteronomy 21:20
They shall say to the elders of his city, ‘This son of ours is stubborn and rebellious, he will not obey us, he is a glutton and a drunkard.’
Proverbs 23:20
Do not be with heavy drinkers of wine, or with gluttonous eaters of meat;
Proverbs 23:21
For the heavy drinker and the glutton will come to poverty, and drowsiness will clothe one with rags.
Proverbs 28:7
He who keeps the law is a discerning son, But he who is a companion of gluttons humiliates his father.
Matthew 11:19
The Son of Man came eating and drinking, and they say, ‘Behold, a gluttonous man and a drunkard, a friend of tax collectors and sinners!’ Yet wisdom is vindicated by her deeds.”
Luke 7:34
The Son of Man has come eating and drinking, and you say, ‘Behold, a gluttonous man and a drunkard, a friend of tax collectors and sinners!’
Titus 1:12
One of themselves, a prophet of their own, said, “Cretans are always liars, evil beasts, lazy gluttons.”
Philippians 3:18-20
For many walk, of whom I often told you, and now tell you even weeping, that they are enemies of the cross of Christ, whose end is destruction,
whose god is their appetite.