late 14c., "of the air, containing air, made of air," from air (n.1) + -y (2).
The meanings "breezy, exposed to the air, open to currents of air; lofty, high; light, buoyant; flimsy; flippant, jaunty, affectedly lofty; vain; unreal" all are attested by late 16c. From 1620s as "done in the air;" 1640s as "sprightly, light in movement;" 1660s as "visionary, speculative." Disparaging airy-fairy "unrealistic, fanciful" is attested from 1920 (earlier in a sense of "delicate or light as a fairy," which is how Tennyson used it in 1830).
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.