mid-15c., "dense, close, compact," from Middle English thight, from Old Norse þettr "watertight, close in texture, solid," from Proto-Germanic *thenkhtuz (cf. second element in Old English meteþiht "stout from eating;" Middle High German dihte "dense, thick," German dicht "dense, tight," Old High German gidigan, German gediegen "genuine, solid, worthy"), from PIE root *tenk- "to become firm, curdle, thicken" (cf. 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; that of "close, sympathetic" is from 1956. 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 1876.