fly (n.) Look up fly at Dictionary.com
Old English fleoge "fly, winged insect," from Proto-Germanic *fleugjon (cognates: Old Saxon fleiga, Old Norse fluga, Middle Dutch vlieghe, Dutch vlieg, Old High German flioga, German Fliege "fly); literally "the flying (insect)" (compare Old English fleogende "flying"), from same source as fly (v.1).

Originally any winged insect (hence butterfly, etc.); long used by farmers and gardeners for any insect parasite. The Old English plural in -n (as in oxen) gradually normalized 13c.-15c. to -s. Fly on the wall "unseen observer" first recorded 1881. An Old English word for "curtain" was fleonet "fly-net." Fly-swatter as a bit of wire mesh on a handle first attested 1917. Fly-fishing is from 1650s.

From the verb and the notion of "flapping as a wing does" comes the noun sense of "tent flap" (1810), which yielded "covering for buttons that close up a garment" (1844). The sense of "a flight, flying" is from mid-15c. Baseball fly ball attested by 1866. To do something on the fly is 1856, apparently from baseball.
When the catcher sees several fielders running to catch a ball, he should name the one he thinks surest to take it, when the others should not strive to catch the ball on the fly, but only, in case of its being missed, take it on the bound. ["The American Boys Book of Sports and Games," New York, 1864]
fly (v.1) Look up fly at Dictionary.com
"to soar through air," Old English fleogan "to fly" (class II strong verb; past tense fleag, past participle flogen), from Proto-Germanic *fleugan "to fly" (cognates: Old Saxon and Old High German fliogan, Old Norse flügja, Old Frisian fliaga, Middle Dutch vlieghen, Dutch vliegen, German fliegen), from PIE *pleu- "flowing, floating" (see pluvial). Related: Flew; flied (baseball); flying. Slang phrase fly off the handle "lose one's cool" dates from 1825.
fly (v.2) Look up fly at Dictionary.com
"run away," Old English fleon (see flee). Fleogan and fleon were often confused in Old English, too. Modern English distinguishes in preterite: flew/fled.
fly (adj.) Look up fly at Dictionary.com
slang, "clever, alert, wide awake," late 18c., perhaps from fly (n.) on the notion of the insect being hard to catch. Other theories, however, trace it to fledge or flash. Slang use in 1990s might be a revival or a reinvention.