late 14c., transitive "to bathe (a person or a body part) in a steam bath," from Old French estuver "have a hot bath, plunge into a bath; stew" (Modern French étuver), of uncertain origin. Common Romanic (cognates: Spanish estufar, Italian stufare), possibly from Vulgar Latin *extufare "evaporate," from ex- "out" + *tufus "vapor, steam," from Greek typhos "smoke." Compare Old English stuf-bæþ "hot-air bath;" see stove.
Intransitive use from 1590s. Meaning "to boil slowly, to cook meat by simmering it in liquid" is attested from early 15c. The meaning "to be left to the consequences of one's actions" is from 1650s, especially in figurative expression to stew in one's own juices. Related: Stewed; stewing. Slang stewed "drunk" first attested 1737.