Old English sihð, gesiht, gesihð "thing seen; faculty of sight; aspect; vision; apparition," from Proto-Germanic *sekh(w)- (cf. Danish sigte, Swedish sigt, Middle Dutch sicht, Dutch zicht, Old High German siht, German Sicht, Gesicht), stem that also yielded Old English seon (see see (v.)), with noun suffix -th (2), later -t.
Meaning "perception or apprehension by means of the eyes" is from early 13c. Meaning "device on a firearm to assist in aiming" is from 1580s. A "show" of something, hence, colloquially, "a great many; a lot" (late 14c.). Sight for sore eyes "welcome visitor" is attested from 1738; sight unseen "without previous inspection" is from 1892. Sight gag first attested 1944. Middle English had sighty (late 14c.) "visible, conspicuous; bright, shining; attractive, handsome;" c.1400 as "keen-sighted;" mid-15c. as "discerning" (cf. German sichtig "visible").