Old English stocc "stump, post, stake, tree trunk, log," also "pillory" (usually plural, stocks), from Proto-Germanic *stukkaz "tree trunk" (cf. Old Norse stokkr "block of wood, trunk of a tree," Old Saxon, Old Frisian stok, Middle Dutch stoc "tree trunk, stump," Dutch stok "stick, cane," Old High German stoc "tree trunk, stick," German Stock "stick, cane;" also Dutch stuk, German Stück "piece"), from PIE *(s)teu- (see steep (adj.)).
Meaning "ancestry, family" (late 14c.) is a figurative use of the "tree trunk" sense (cf. family tree). This is also the root of the meaning "heavy part of a tool," and "part of a rifle held against the shoulder" (1540s). Stock, lock, and barrel "the whole of a thing" is recorded from 1817. Meaning "framework on which a boat was constructed" (early 15c.) led to figurative phrase on stocks "planned and commenced" (1660s). Stock-still (late 15c.) is literally "as still as a tree trunk."