Nälkä kasvaa syödessä / The hunger grows by eating
The more you eat, the more you crave, the English equivalent would probably be “I am a bottomless pit”. This applies also to other good things in life besides food.
Apparently the same idea exists in French “L’appétit vient en mangeant.”
On the other hand “ei makeaa mahan täydeltä” / “don’t fill your stomack with sweets” means that you shouldn’t have too much good things.
Hänellä on ketunhäntä kainalossa.
He has a fox tail under his arm.
The cunning fox is a metaphor for dishonesty, so hiding a fox tail refers to somekind of dodgyness. A similar idiom exists in English: “a wolf in sheep’s clothing”, and it’s also a common saying in Finnish: “Hän on susi lammasten vaatteissa.”
Another idiom related to suspicious things is “Juttuun oli koira haudattuna.” / “There’s a dog buried in it.” In English, you’d probably say something like “there’s something fishy about it” or “I smell a rat.”