c. 1400, tyght "dense, close, compact," from Middle English thight, from Old Norse þettr "watertight, close in texture, solid," and also from Old English -þiht (compare second element in meteþiht "stout from eating"), both from Proto-Germanic *thinhta- (source also of Middle High German dihte "dense, thick," German dicht "dense, tight," Old High German gidigan, German gediegen "genuine, solid, worthy"), from PIE root *tenk- (2) "to become firm, curdle, thicken" (source also of Irish techt "curdled, coagulated," Lithuanian tankus "close, tight," Persian tang "tight," Sanskrit tanakti "draws together, contracts").
Sense of "drawn, stretched" is from 1570s; meaning "fitting closely" (as of garments) is from 1779; that of "evenly matched" (of a contest, bargain, etc.) is from 1828, American English; that of "drunk" is from 1830. Of persons, "close, intimate, sympathetic" from 1956. From 1670s as an adverb; to sit tight is from 1738; sleep tight as a farewell in sending someone off to bed is by 1871. Related: Tightly; tightness. Tight-assed "unwilling to relax" is attested from 1903. Tight-laced is recorded from 1741 in both the literal and figurative senses. Tight-lipped is first attested 1872.
also screw-driver, "tool like a blunt chisel which fits into the nick in the head of a screw and is used to turn it," 1779, from screw (n.) + driver. Meaning "cocktail made from vodka and orange juice" is recorded from 1956. (Screwed/screwy have had a sense of "drunk" since 19c.; compare slang tight "intoxicated," or perhaps the notion is "twisted").