If this is correct, the sense development would be from "loft, ceiling" to "sky, air." Buck suggests a further connection with Old High German louft "bark," louba "roof, attic," etc., with development from "bark" to "roof made of bark" to "ceiling," though this did not directly inform the meaning "air, sky" (compare lodge (n.)). But Watkins says this is "probably a separate Germanic root." Meaning "gallery in a church" first attested c. 1500. From 1520s as "apartment over a stable" used for hay storage, etc.
1866, originally in reference to surfaces such as shell casings of beetle wings, from French aéroplane (1855), from Greek-derived aero- "air" (see air (n.1)) + stem of French planer "to soar," from Latin planus "level, flat" (from PIE root *pele- (2) "flat; to spread").
The word was later extended to the wing of a heavier-than-air flying machine. The use of the word in reference to the machine itself is first attested 1873 and probably is an independent coinage in English. Also see airplane. Ancient Greek had a word aeroplanos, but it meant "wandering in the air," from planos "wandering" (see planet).
Meaning "go at full speed" is from c. 1300. In reference to flags, 1650s. Transitive sense "cause to move or float in air" (as a flag, kite, etc.) is from 1739; sense of "convey through the air" ("Fly Me to the Moon") is from 1864. Related: Flew; flied (baseball); flown; flying. Slang phrase fly off the handle "lose one's cool" dates from 1825.