From Middle English greve, from Old English grǣfe, græfe, probably related to Proto-Germanic *grōbō. Cognate with Scots greve, greave. Compare also Proto-Germanic *grainiz ("twig"), of unknown origin, whence Old Norse grein ("branch, bough"). Closely related to Old English grāf, grāfa. See grove.
From Middle English greve, greyve, from Old English grǣfa, grēfa, from Proto-Germanic *grōbō ("pit, ditch"), from Proto-Indo-European *gʰrebʰ- ("to dig, scratch, scrape"). Cognate with North Frisian groop ("pit, sewer, gutter"), Dutch groef ("pit, hole, gutter"), German Grube ("pit, hole"), Icelandic gröf ("pit, grave").
From Middle English greve, grayve, from Old French greve ("shin"), of uncertain origin; possibly from Egyptian Arabic جورب ("stocking, leg cover"). Watkins suggests a connection with greve, due to the resemblance of the medial ridge to a part in the hair, from graver, of Germanic origin, from Frankish *graban; if so, related to Etymology 2 above.