"enclosure," Old English haga "enclosure, hedge," from Proto-Germanic *hag- (cf. Old Norse hagi, Old Saxon hago, German Hag "hedge;" Middle Dutch hage, Dutch haag, as in the city name The Hague). See hag and hedge. Meaning "fruit of the hawthorn bush" (Old English) is perhaps short for *hægberie.
"hesitate in speech," 1580s, imitative. Related: Hawed; hawing. The noun in this sense is from c.1600. Haw-haw "style of affected enunciation" is from 1841, imitative.