The sense of "accustom a child to not suckling from the breast" in Old English generally was expressed by gewenian or awenian, which has a sense of "unaccustom" (compare German abgewöhnen, entwöhnen "to wean," literally "to unaccustom"). The modern word might be one of these with the prefix worn off, or it might be wenian in a specialized sense of "accustom to a new diet." Figurative extension to any pursuit or habit is from 1520s.
It forms all or part of: vanadium; Vanir; venerate; veneration; venerable; venereal; venery (n.1) "pursuit of sexual pleasure;" venery (n.2) "hunting, the sports of the chase;" venial; venison; venom; Venus; wean; ween; Wend "Slavic people of eastern Germany;" win; winsome; wish; wont; wynn.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit veti "follows after," vanas- "desire," vanati "desires, loves, wins;" Avestan vanaiti "he wishes, is victorious;" Latin venerari "to worship," venus "love, sexual desire; loveliness, beauty;" Old English wynn "joy," wunian "to dwell," wenian "to accustom, train, wean," wyscan "to wish."
c. 1300, from Anglo-French severer, Old French sevrer "to separate" (12c., later in French restricted to "to wean," i.e. "to separare from the mother"), from Vulgar Latin *seperare, from Latin separare "to pull apart," from se- "apart" (see secret (n.)) + parare "make ready, prepare" (from PIE root *pere- (1) "to produce, procure").