1590s, Shakespearean back-formation from groveling "on the face, prostrate" (mid-14c.), also used in Middle English as an adjective but probably really an adverb, from gruffe, from Old Norse grufe "prone" + obsolete adverbial suffix -ling (which survives also as the -long in headlong, sidelong). The Old Norse word is found in liggja à grufu "lie face-down," literally "lie on proneness." Old Norse also had grufla "to grovel," grufa "to grovel, cower, crouch down." The whole group is perhaps related to creep (v.). Related: Groveled; grovelled; groveling; grovelling.
Middle English faunen, from Old English fagnian "rejoice, be glad, exult, applaud," from fægen "glad" (see fain); used in Middle English to refer to expressions of delight, especially a dog wagging its tail (early 14c.), hence "court favor, grovel, act slavishly" (early 15c.). Related: Fawned; fawning.