Etymology
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hag (n.)
early 13c., "repulsive old woman" (rare before 16c.), probably from Old English hægtes, hægtesse "witch, sorceress, enchantress, fury," shortened on the assumption that -tes was a suffix. The Old English word is from Proto-Germanic *hagatusjon, which is of unknown origin. Dutch heks, German Hexe "witch" are similarly shortened from cognate Middle Dutch haghetisse, Old High German hagzusa.

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.
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hag-ridden (n.)

1680s, "ridden by hags or witches," past-participle adjective from hag-ride (1660s); see hag (n.) + ridden. From 1702 as "oppressed, harassed;" 1758 as "afflicted by nightmares." An old term for sleep paralysis (the sensation of being held immobile in bed, often by a heavy weight, and accompanied by a sense of alien presence). A holed stone hung over the bed was said to prevent it.

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hagged (adj.)
c. 1700, from hag, by influence of haggard. Originally "bewitched," also "lean, gaunt," as bewitched persons and animals were believed to become.
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haw (n.)
"enclosure," Old English haga "enclosure, fortified enclosure; hedge," from Proto-Germanic *hag- (source also of Old Norse hagi, Old Saxon hago, German Hag "hedge;" Middle Dutch hage, Dutch haag, as in the city name The Hague), from PIE root *kagh- "to catch seize; wickerwork fence" (see hedge (n.), and compare hag). Meaning "fruit of the hawthorn bush" (Old English) is perhaps short for *hægberie.
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hex (v.)

1830, American English, from Pennsylvania German hexe "to practice witchcraft," from German hexen "to hex," related to Hexe "witch," from Middle High German hecse, hexse, from Old High German hagazussa (see hag). Noun meaning "magic spell" is first recorded 1909; earlier it meant "a witch" (1856). Compare Middle English hexte "the devil" (mid-13c.), perhaps originally "sorcerer," probably from Old English haehtis.

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haggard (adj.)

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.

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fag (n.2)
shortening of faggot (n.2) "male homosexual," by 1921. Fag hag "heterosexual woman who keeps company with gay men" attested by 1969.
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hagiology (n.)
"branch of literature consisting of saints' lives and legends," 1807, from hagio- "holy" + -ology. Related: Hagiologist (1805).
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Haggadah (n.)
"saying in the Talmud illustrative of the law," 1856, from Rabbinical Hebrew haggadhah, literally "tale," verbal noun from higgidh "to make clear, narrate, expound." Plural Haggadoth. Related: Haggadic.
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hagio- 
before vowels hagi-, word-forming element meaning "of a saint, saintly, holy," from Greek hagios "sacred, devoted to the gods" (of things), "holy, pure" (of persons), in Ecclesiastical Greek, "a saint," which is perhaps from PIE *yag- "to worship, reverence" (source also of Greek agnos "chaste," Sanskrit yajati "reveres (a god) with sacrifices, worships," Old Persian ayadana "temple").
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