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).
1580s, "to get drunk" (intransitive); c. 1600, "to confuse as though with drink" (transitive), of obscure origin, perhaps from Low German fuddeln "work in a slovenly manner (as if drunk)," from fuddle "worthless cloth." The more common derivative befuddle dates only to 1873. Related: Fuddled; fuddling. A hard-drinker in 17c. might be called a fuddle-cap (1660s).
<a href="https://www.etymonline.com/word/befuddle">Etymology of befuddle by etymonline</a>
Harper, D. (n.d.). Etymology of befuddle. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/befuddle