word-forming element of verbs and nouns from verbs, with a wide range of meaning: "about, around; thoroughly, completely; to make, cause, seem; to provide with; at, on, to, for;" from Old English be- "about, around, on all sides" (the unstressed form of bi "by;" see by (prep.)). The form has remained by- in stressed positions and in some more modern formations (bylaw, bygones, bystander).
The Old English prefix also was used to make transitive verbs and as a privative prefix (as in behead). The sense "on all sides, all about" naturally grew to include intensive uses (as in bespatter "spatter about," therefore "spatter very much," besprinkle, etc.). Be- also can be causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, such as bethwack "to thrash soundly" (1550s) and betongue "to assail in speech, to scold" (1630s).
mid-12c., from Old French guile "deceit, wile, fraud, ruse, trickery," probably from Frankish *wigila "trick, ruse" or a related Germanic source, from Proto-Germanic *wih-l- (source also of Old Frisian wigila "sorcery, witchcraft," Old English wig "idol," Gothic weihs "holy," German weihen "consecrate"), from PIE root *weik- (2) "consecrated, holy."