Origin: before 1150 for an earlier sense; Middle English we, variant of wei (small) quantity, Old English wēg, 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."