Nip
late Middle English: probably of Low German or Dutch origin.
wiktionary
Short for nipperkin, ultimately from Middle Low German nippen or Middle Dutch nipen("to sip; nip"; > Dutch nippen). Compare also German nippen(“to sip; taste”).
Clipping of nipple.
From late Middle English nippen, probably of Low German or Dutch origin, probably a byform of earlier *knippen (suggested by the derivative Middle English knippette(“pincers”)), ultimately from Proto-Germanic *knīpaną(“to pinch”); related to Dutch nijpen, knijpen(“to pinch”), Danish nive(“pinch”); Swedish nypa(“pinch”); Low German knipen; German kneipen and kneifen(“to pinch, cut off, nip”), Old Norse hnippa(“to prod, poke”); Lithuanian knebti.
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
etymonline
nip (v.)
late 14c., nippen, "to pinch sharply; to bite suddenly," probably from or related to Middle Low German nipen "to nip, to pinch," German nippen, Middle Dutch nipen "to pinch," Dutch nijpen, Old Norse hnippa "to prod," but the exact evolution of the stem is obscure. Related: Nipped; nipping.
Meaning "break off the tip by pinching" is from c. 1400. Sense of "blast as by frost, check the growth or vigor of" is from 1580s. To nip (something) in the bud in the figurative sense of "kill or destroy in the first stage of growth" is recorded from c. 1600. Slang nip in, nip out, etc., in which the sense of the verb is "move rapidly or nimbly" is attested from 1825.
nip (n.1)
"small measure of strong spirits," 1796, slang shortening of nipperkin (1670s) "quantity of beer or liquor of a half pint or less," possibly of Dutch or Low German origin (compare German Nipp "sip, taste") and related to nip (v.). Reinforced by nip (n.2) in its secondary sense of "fragment or bit pinched off" (c. 1600).
nip (n.2)
"a pinch; a sharp bite," 1540s, from nip (v.). Sense of "a small bit of anything, fragment or bit pinched off" is from c. 1600. Meaning "a chill in the weather" is from 1610s, probably so called for its effect on vegetation. Nip and tuck "a close thing," especially a close approach to equality in the results of a horse race or any competition, is recorded by 1847, American English, perhaps an image from sailing or tailoring.