late 14c., overloken, "to examine carefully, scrutinize, inspect," from over- + look (v.). Another Middle English sense was "to peer over the top of, survey from on high, view from a high place" (c. 1400).
These two literal senses have given rise to the two main modern meanings. The meaning "to look over or beyond and thus fail to see" (hence "to pass over indulgently") is via the notion of "to choose to not notice" and is attested from 1520s. The seemingly contradictory sense of "to watch over officially, keep an eye on, superintend" is from 1530s. Related: Overlooked; overlooking. In Shakespeare's day, overlooking also was a common term for "inflicting the evil eye on" (someone or something). Middle English had oure-loker (over-looker), meaning "a timekeeper in a monastery" (early 15c.).