> be-
word-forming element with a wide range of meaning: "thoroughly, completely; to make, cause seem; to provide with; at, on, to, for," from Old English be- "on all sides" (also used to make transitive verbs and as a privative or intensive prefix), from weak form of Old English bi "by," probably cognate with second syllable of Greek amphi, Latin ambi and originally meaning "about" (see ambi-).
This sense naturally drifted into intensive (as in bespatter "spatter about," therefore "spatter very much"). Be- can also be privative (as in behead), causative, or have just about any sense requi…