Old English sihð, gesiht, gesihð "thing seen; faculty of sight; aspect; vision; apparition," from Proto-Germanic *sekh(w)- (source also of 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.
Verily, truth is sight. Therefore if two people should come disputing, saying, 'I have seen,' 'I have heard,' we should trust the one who says 'I have seen.' [Brhadaranyaka Upanishad 5.14.4]
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" (compare German sichtig "visible").