Old English seon "to see, look, behold; observe, perceive, understand; experience, visit, inspect" (contracted class V strong verb; past tense seah, past participle sewen), from Proto-Germanic *sekhwanan (cf. Old Saxon, Old High German sehan, Middle High German, German sehen, Old Frisian sia, Middle Dutch sien, Old Norse sja, Gothic saihwan), from PIE root *sekw- (2) "to see," which is probably identical with *sekw- (1) "to follow" (see sequel), a root which produced words for "say" in Greek and Latin, and also words for "follow" (cf. Latin sequor), but "opinions differ in regard to the semantic starting-point and sequences" [Buck]. Thus see might originally mean "follow with the eyes."
Used in Middle English to mean "behold in the imagination or in a dream" (c.1200), "to recognize the force of (a demonstration)," also c.1200. Sense of "escort" (e.g. to see someone home) first recorded 1607 in Shakespeare. Meaning "to receive as a visitor" is attested from c.1500. Gambling sense of "equal a bet" is from 1590s. See you as a casual farewell first attested 1891. Let me see as a pausing statement is recorded from 1510s. To have seen everything as a hyperbolic expression of astonishment is from 1957.