Origin: before 1150 for an earlier sense; Middle Englishwe, variant of wei (small) quantity, Old Englishwēg, Anglian form of wǣge weight, akin to wegan to weigh1
"extremely small," c.1450, from earlier noun use in sense of "quantity, amount" (cf. a littel wei "a little thing or amount," c.1300), from O.E. wæge "weight" (see weigh). Adj. use wee bit apparently developed as parallel to such forms as a bit thing "a little thing."
Wee hours is attested by 1891, from Scot. wee sma' hours (1787, Burns). Wee folk "faeries" is recorded from 1819. Weeny "tiny, small" is from 1790.