Entries linking to Luftwaffe
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.
Old English wæpen "instrument of fighting and defense, sword," also "penis," from Proto-Germanic *wēipna- (source also of Old Saxon wapan, Old Norse vapn, Danish vaaben, Old Frisian wepin, Middle Dutch wapen, Old High German wafan, German Waffe "weapon"), a word of unknown origin with no cognates outside Germanic; possibly a substratum word.