colloquial for "sleep," 1899, from shut (v.) + eye (n.). Hans Christian Andersen's "Ole Shut-eye," about a being who makes children sleepy, came out 1842; "The Shut-Eye Train" popular children's poem by Eugene Field, is from 1896.
Old English scyttan "to put (a bolt) in place so as to fasten a door or gate, bolt, shut to; discharge, pay off," from West Germanic *skutjan (source also of Old Frisian schetta, Middle Dutch schutten "to shut, shut up, obstruct"), from PIE root *skeud- "to shoot, chase, throw." Related: Shutting.
Meaning "to close by folding or bringing together" is from mid-14c. Meaning "prevent ingress and egress" is from mid-14c. Sense of "to set (someone) free (from)" (c. 1500) is obsolete except in dialectal phrases such as to get shut of. To shut (one's) mouth "desist from speaking" is recorded from mid-14c.
c. 1200, from Old English ege (Mercian), eage (West Saxon) "eye; region around the eye; apperture, hole," from Proto-Germanic *augon (source also of Old Saxon aga, Old Frisian age, Old Norse auga, Swedish öga, Danish øie, Middle Dutch oghe, Dutch oog, Old High German ouga, German Auge, Gothic augo "eye"). Apparently the Germanic form evolved irregularly from PIE root *okw- "to see."
HAMLET: My father — methinks I see my father.
HORATIO: Where, my lord?
HAMLET: In my mind's eye, Horatio.
Until late 14c. the English plural was in -an, hence modern dialectal plural een, ene. Of potatoes from 1670s. Of peacock feathers from late 14c. As a loop used with a hook in fastening (clothes, etc.) from 1590s. The eye of a needle was in Old English. As "the center of revolution" of anything from 1760. Nautical in the wind's eye "in the direction of the wind" is from 1560s.
To see eye to eye is from Isaiah lii.8. Eye contact attested from 1953. To have (or keep) an eye on "keep under supervision" is attested from early 15c. To have eyes for "be interested in or attracted to" is from 1736; make eyes at in the romance sense is from 1837; gleam in (someone's) eye (n.) "barely formed idea" is from 1959. Eye-biter was an old name for "a sort of witch who bewitches with the eyes."