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 *sehwanan (source also of 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" (such as 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" (as in 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.
c. 1300, "throne of a bishop, archbishop, or pope," also "throne of a monarch, a goddess, Antichrist, etc.," from Old French sie "seat, throne; town, capital; episcopal see," from Latin sedem (nominative sedes) "seat, throne, abode, temple," related to sedere "to sit," from PIE root *sed- (1) "to sit." Early 14c. as "administrative center of a bishopric;" c. 1400 as "province under the jurisdiction of a bishop."