quirk (n.) 1560s, “quibble, evasion,” of unknown origin; perhaps originally a technical term for a twist or flourish in weaving. Sense of “peculiarity” is c.1600.
I have to admit my interest here is quite personal, since our family descends from the Quirks, of Irish origin, who settled in Quyon, Quebec. I kid you not.
The word itself is another of those mysteries, emerging in the late Renaissance and, according to OED (as above) originally used in the sense of an evasion or a quibble; later evolving into the notion of the peculiar, usually understood to be an especially charming peculiarity. It’s also often used in the sense of the unique or the original.
Warp, swift, raddle, heddle, sleying, are also all technical terms associated with weaving – warp, interestingly enough, from the verb form (grounded in Old Saxon and Middle Old German) meaning “to bend, twist, distort” and thus, in some ways, sharing a sensibility for the particular and peculiar flourish that once defined a quirk.