"bundle of fiber in a lamp or candle," Old English weoce, from West Germanic *weukon (cf. Middle Dutch wieke, Dutch wiek, Old High German wiohha, German Wieche), of unknown origin, with no known cognates beyond Germanic. To dip one's wick "engage in sexual intercourse" (in reference to males) is recorded from 1958, perhaps from Hampton Wick, rhyming slang for "prick," which would connect it rather to wick (n.2).
"dairy farm," now surviving, if at all, as a localism in East Anglia or Essex, it was once the common Old English wic "dwelling place, lodging, abode," then coming to mean "village, hamlet, town," and later "dairy farm" (e.g. Gatwick "Goat-farm"). Common in this latter sense 13c.-14c. The word is a general Germanic borrowing from Latin vicus "group of dwellings, village; a block of houses, a street, a group of streets forming an administrative unit" (see vicinity). Cf. Old High German wih "village," German Weichbild "municipal area," Dutch wijk "quarter, district," Old Frisian wik, Old Saxon wic "village."