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).
wig n.
1670s, shortened form of periwig. Meaning "person who wears a wig (professionally)" is from 1828.
wig v.
1826, "supply with a wig," from wig (n.). The earlier verb was bewig (see bewigged). The meaning "to behave hysterically" (usually with out) is attested from 1955, perhaps from notion in flip one's wig. Compare dash my wig!, a former mild imprecation (1797), also wigs on the green (1856), Irish colloquial for "a fight or rumble" (because wigs are likely to get detached from owners in such an event). The verb also had a colloquial sense of "scold severely," attested by 1829, perhaps related to these. Related: Wigged; wigging.