Etymology
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see (v.)

Middle English sēn, from Old English seon (Anglian sean) "be or become aware of by means of the eye; look, behold;" also "perceive mentally, understand; experience; visit (a place); 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).

This is reconstructed to be from PIE root *sekw- (2) "to see." That PIE root often was said to be probably identical with *sekw- (1) "to follow," 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 mean, etymologically, "follow with the eyes" (and in some languages extending to "speak, say, tell"). But OED finds this "involves a hypothetical sense-development which it is not easy to accept with confidence," and Boutkan also doubts the connection and gives the word "No certain PIE etymology." 

It is attested by late Old English as "be able to see with the eyes, have the faculty of sight, not be blind."

As the sense of sight affords far more complete and definite information respecting external objects than any other of the senses, mental perceptions are in many (perh. in all) languages referred to in visual terms, and often with little or no consciousness of metaphor. [OED]

English see has been used in many of these senses since early Middle English: "foresee; behold in the imagination or in a dream," also "to recognize the force of (a demonstration)," all c. 1200.

It is attested by c. 1300 as "ensure, make sure" (something is so, someone does something). To see to is by late 14c. as "be attentive to, take special care about" (also "to look at"); hence "attend to, arrange for, bring about as a result." See to it "take special care; see that it be done" is from late 15c.

The sense of "escort" (as in see you home) is attested c. 1600 in Shakespeare. The meaning "to receive as a visitor" is attested from c. 1500. The wagering sense of "equal a bet, accept by staking a similar sum" is by 1590s. Used in phrases expressing comparative and superlative (best I've ever seen) from early 14c.

Imperative use of see! "look! behold!" is by early 14c. Emphatic expression see here is attested from early 15c.; probably the notion is "see, here is ...;" but the modern use of it as "a brusque form of address used to preface an order," etc. [OED] is by 1897 in schoolboy talk. The qualifying expression as far as I can see is attested from 1560s.

Let me see as a statement expressing consideration when the speaker is trying to recall something is recorded from 1510s. See you as a casual farewell is attested by 1891 (see you soon; probably short for hope to see you soon). To see something in (someone, etc.) "perceive good or attractive qualities in" is by 1832.

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see (n.)

c. 1300, "throne of a bishop, archbishop, or pope," also "throne of a monarch, a goddess, the 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").

Attested by early 14c. as "administrative center of a bishopric;" c. 1400 as "province under the jurisdiction of a bishop." In Middle English also sometimes simply "place to sit, a chair" (late 14c.).

It differs from diocese, however, in that diocese represents the territorial province for the care of which the bishop is responsible (that is, where his duties lie), whereas see is the local seat of his authority, dignity, and episcopal privileges. [Century Dictionary]
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look-see (n.)
"inspection," 1865, "Pidgin-like formation" [OED], first used in representations of English as spoken by Chinese, from look (v.) + see (v.).
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see-through (adj.)

1950, from the verbal phrase, "see things on the other side of" (c. 1400); see see (v.) + through (adv.). The verbal phrase see through often is figurative, "perceive the real character of, detect imposture." To see (something) through "continue with until the end" is by 1828 (to see (something) out in the same sense is from 1782).

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see-saw (v.)
also seesaw, "move up and down," 1712, from see-saw (n.). Related: See-sawed; see-sawing.
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see-saw (n.)

also seesaw, 1630s, in see-saw-sacke a downe (like a Sawyer), words in a rhythmic jingle used by children and repetitive-motion workers, probably imitative of the rhythmic back-and-forth motion of sawyers working a two-man pit saw (see saw (n.1). Ha ha.).

In reference to a children's sport of going alternately up and down on a plank balanced on some support, it is recorded from 1704; the figurative sense of this is from 1714. Applied from 1824 to the plank arranged and adjusted for the game. Also compare teeter-totter under teeter (v.). 

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saw (v.)
past tense of see; from Old English plural sawon.
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seeing (n.)

"action or fact of perceiving with the eyes or mind," verbal noun from see (v.). Expression seeing is believing is attested by 1660s.

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sightseeing (n.)
also sight-seeing, 1821, from sight (see sights) + present participle of see (v.). Sight-see (v.) is from 1824. Sight-seer first recorded 1821.
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seeing (adj.)

"perceiving with the eyes or mind, looking, beholding," c. 1300, present-participle adjective from see (v.). Seeing Eye dog is attested by 1929, American English, trademarked by Seeing Eye Inc. of New Jersey.

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