Twig

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Old English twigge, of Germanic origin; related to Dutch twijg and German Zweig, also to twain and two.

wiktionary

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From Middle English twig, twyg, from Old English twiġ, from Proto-Germanic *twīgą (compare West Frisian twiich, Dutch twijg, German Zweig), from Proto-Indo-European *dweygʰom (compare Old Church Slavonic двигъ(dvigŭ, “branch”), Albanian degë(“branch”)), from *dwóh₁. More at two.

From Irish and Scottish Gaelic tuig(“to understand”).

Compare tweak.

etymonline

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twig (n.)

Old English twig "twig, branch, shoot, small tree," from Proto-Germanic *twigga "a fork" (source also of Middle Dutch twijch, Dutch twijg, Old High German zwig, German Zweig "branch, twig"), from PIE *dwi-ko-, from root *dwo- "two." Compare Old English twisel "fork, point of division."