batty adj.

flying mouse-like mammal (order Chiroptera), 1570s, a dialectal alteration of Middle English bakke (early 14c.), which is probably related to Old Swedish natbakka, Old Danish nathbakkæ "night bat," and Old Norse leðrblaka "bat," literally "leather flapper," from Proto-Germanic *blak-, from PIE root *bhlag- "to strike" (see flagellum).

If so, the original sense of the animal name likely was "flapper." The shift from -k- to -t- may have come through confusion of bakke with Latin blatta "moth, nocturnal insect."

The Old English word for the animal was hreremus, from hreran "to shake" (see rare (adj.2)), and rattle-mouse, an old dialectal word for "bat," is attested from late 16c. Flitter-mouse (1540s) occasionally is used in English (with variants flinder-mouse, flicker-mouse) in imitation of German fledermaus "bat," from Old High German fledaron "to flutter."

As a contemptuous term for an old woman, it is perhaps a suggestion of witchcraft (compare fly-by-night), or from bat as "prostitute who plies her trade by night" [Farmer, who calls it "old slang" and finds French equivalent "night swallow" (hirondelle de nuit) "more poetic"].

adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.

also bat-shit, by 1967 as a variant of bullshit (n.) in the slang sense; from bat (n.2) + shit (n.). By early 1980s as "crazy," the sense shift is for uncertain reasons; perhaps (these are very long shots) from the notion of guano as an explosive or health problems caused by inhaling powdered bat feces in caves and mines. Also compare batty "crazy" (early 20c.), from the expression bats in (one's) belfry.