Old English hecg "hedge," originally any fence, living or artificial, from West Germanic *hagjo (source also of Middle Dutch hegge, Dutch heg, Old High German hegga, German Hecke "hedge"), from a verb *hagjanan, from PIE root *kagh- "to catch, seize; wickerwork, fence" (source also of Latin caulae "a sheepfold, enclosure," Gaulish caio "circumvallation," Welsh cae "fence, hedge"). Related to Old English haga "enclosure, hedge" (see haw (n.)).
Figurative sense of "boundary, barrier" is from mid-14c. As hedges were "often used by vagabonds as places of shelter or resort" [Century Dictionary], the word, compounded, "notes something mean, vile, of the lowest class" [Johnson], from contemptuous attributive sense of "plying one's trade under a hedge" (hedge-priest, hedge-lawyer, hedge-wench, etc.), a usage attested from 1530s. The noun in the betting sense is from 1736 (see hedge (v.)).
"landing place, place where vessels are loaded and unloaded, a wharf," 1690s, a spelling variant of Middle English key, keye, caye "wharf" (c. 1300; mid-13c. in place names), from Old North French cai (Old French chai, 12c., Modern French quai) "sand bank," from Gaulish caium (5c.), from Old Celtic *kagio- "to encompass, enclose" (source also of Welsh cae "fence, hedge," Cornish ke "hedge"), from PIE root *kagh- "to catch, seize; wickerwork, fence" (see hedge (n.)). Spelling altered in English by influence of French quai.
1560s, "wild, unruly" (originally in reference to hawks), from French haggard, probably from Old French faulcon hagard "wild falcon," literally "falcon of the woods," from hagard, hagart, from Middle High German hag "hedge, copse, wood," from Proto-Germanic *hagon, from PIE root *kagh- "to catch, seize;" also "wickerwork, fence" (see hedge (n.)). OED, however, finds this derivation "very doubtful." Sense perhaps reinforced by Low German hager "gaunt, haggard." Sense of "with a haunted and wild expression" first recorded 1690s; that of "careworn" first recorded 1853. Sense influenced by association with hag. Related: Haggardly; haggardness.
The first element probably is cognate with Old English haga "enclosure, portion of woodland marked off for cutting" (see hedge (n.)). Old Norse had tunriða and Old High German zunritha, both literally "hedge-rider," used of witches and ghosts. The second element in the prehistoric compound may be connected with Norwegian tysja "fairy; crippled woman," Gaulish dusius "demon," Lithuanian dvasia "spirit," from PIE *dhewes- "to fly about, smoke, be scattered, vanish."
One of the magic words for which there is no male form, suggesting its original meaning was close to "diviner, soothsayer," which were always female in northern European paganism, and hægtesse seem at one time to have meant "woman of prophetic and oracular powers" (Ælfric uses it to render the Greek "pythoness," the voice of the Delphic oracle), a figure greatly feared and respected. Later, the word was used of village wise women.
Haga is also the haw- in hawthorn, which is an important tree in northern European pagan religion. There may be several layers of folk etymology here. Confusion or blending with heathenish is suggested by Middle English hæhtis, hægtis "hag, witch, fury, etc.," and haetnesse "goddess," used of Minerva and Diana.
If the hægtesse once was a powerful supernatural woman (in Norse it is an alternative word for Norn, any of the three weird sisters, the equivalent of the Fates), it might originally have carried the hawthorn sense. Later, when the pagan magic was reduced to local scatterings, it might have had the sense of "hedge-rider," or "she who straddles the hedge," because the hedge was the boundary between the civilized world of the village and the wild world beyond. The hægtesse would have a foot in each reality. Even later, when it meant the local healer and root collector, living in the open and moving from village to village, it may have had the mildly pejorative Middle English sense of hedge- (hedge-priest, etc.), suggesting an itinerant sleeping under bushes. The same word could have contained all three senses before being reduced to its modern one.