Old English sceort, scort "short, not long, not tall; brief," probably from Proto-Germanic *skurta- (source also of Old Norse skorta "to be short of," skort "shortness;" Old High German scurz "short"), from PIE root *sker- (1) "to cut," on the notion of "something cut off" (compare Sanskrit krdhuh "shortened, maimed, small;" Latin curtus "short," cordus "late-born," originally "stunted in growth;" Old Church Slavonic kratuku, Russian korotkij "short;" Lithuanian skursti "to be stunted," skardus "steep;" Old Irish cert "small," Middle Irish corr "stunted, dwarfish," all from the same root).
Meaning "having an insufficient quantity" is from 1690s. Meaning "rude" is attested from late 14c. Meaning "easily provoked" is from 1590s; perhaps the notion is of being "not long in tolerating."
Short fuse in figurative sense of "quick temper" first attested 1968. To fall short is from archery. Short run "relatively brief period of time" is from 1879. Short story first recorded 1877. Short cut is from 1580s, from cut (n.) in the sense "passage, course, or way straight across" (1570s).
To make short work of "dispose of quickly" is first attested 1570s. Phrase short and sweet is from 1530s. To be short by the knees (1733) was to be kneeling; to be short by the head (1540s) was to be beheaded.