1590s, "manner, appearance" (as in an air of mystery); 1650s, "assumed manner, affected appearance" (especially in phrase put on airs, 1781), from French air "look, appearance, mien, bearing, tone" (Old French aire "reality, essence, nature, descent, extraction" (12c.); compare debonair), which is perhaps from Latin ager "place, field, productive land" (from PIE root *agro- "field") on notion of "place of origin."
But some French sources connect this Old French word with the source of air (n.1), and it also is possible these senses in English developed from or were influenced by air (n.1); compare sense development of atmosphere and Latin spiritus "breath, breeze," also "high spirit, pride," and the extended senses of anima.
<a href="https://www.etymonline.com/word/airs">Etymology of airs by etymonline</a>
Harper, D. (n.d.). Etymology of airs. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/airs