1590s, fusse, first attested in fusball "puff ball of tiny spores," of uncertain origin; perhaps a back-formation from fuzzy, if that word is older than the record of it. Meaning "the police" is American English, 1929, underworld slang; origin, signification, and connection to the older word unknown. Perhaps a variant of fuss, with a notion of "hard to please."

1702, "make fuzzy," from fuzz, n.. Related: Fuzzed; fuzzing. Fuzzword (based on buzzword) "deliberately confusing or imprecise bit of jargon" is a coinage in political writing from 1983.