peyH-
“to be fat, to swell”fat, swell, abound
Root for fatness/swelling, yielding Greek pion (fat), Latin pinguis, English fat, pine (tree).
Discussion
The PIE root *peyH- (to be fat, to swell, to be full of substance) produced vocabulary for fatness, abundance, and the products of fattened animals — connecting bodily fullness to economic prosperity.
Latin pīnus (pine tree — the resinous/fat tree, full of sap) and the related pītuīta (phlegm, mucus — fatty bodily fluid) gave English: pine (the tree), pitch (from the tree's resin), and pituitary (the gland named for its mucous secretions).
Greek pī́ōn (πίων, "fat, rich, fertile") and the related pī́ar (fat, grease) preserve the root in the Hellenic branch.
Sanskrit páyate ("he swells, he fills") and pívas- ("fat, sap") confirm the Indo-Iranian reflex.
The root connects to *pewH- (to purify — see the pure/purge root) through a possible semantic link between fatness and quality: what is fat is full, what is full is rich, what is rich is pure/good. This equation of fatness with prosperity appears across IE cultures — a well-fed animal is a valuable animal, and the fat of the land is its best produce.
English fat itself is NOT from this root (it descends from a different PIE form *poyd-), but the conceptual territory is shared.
Notes
Pokorny 793-794. English fat, fir, pine, pitch (resin), pituitary.