wing (n.) Look up wing at Dictionary.com
late 12c., wenge, from Old Norse vængr "wing of a bird, aisle, etc." (cognates: Danish and Swedish vinge "wing"), of unknown origin, perhaps from a Proto-Germanic *we-ingjaz, suffixed form of PIE root *we- "blow" (source of Old English wawan "to blow;" see wind (n.)). Replaced Old English feðra (plural) "wings" (see feather). The meaning "either of two divisions of a political party, army, etc." is first recorded c.1400; theatrical sense is from 1790.

The slang sense of earn (one's) wings is 1940s, from the wing-shaped badges awarded to air cadets on graduation. To be under (someone's) wing "protected by (someone)" is recorded from early 13c. Phrase on a wing and a prayer is title of a 1943 song about landing a damaged aircraft.
wing (v.) Look up wing at Dictionary.com
c.1600, "take flight;" 1610s, "fit with wings," from wing (n.). Meaning "shoot a bird in the wing" is from 1802, with figurative extensions to wounds suffered in non-essential parts. Verbal phrase wing it (1885) is said to be from a theatrical slang sense of an actor learning his lines in the wings before going onstage, or else not learning them at all and being fed by a prompter in the wings; but perhaps it is simply an image of a baby bird taking flight from the nest for the first time (the phrase is attested in this sense from 1875). Related: Winged; winging.