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past participle adjective from feed (v.). Fed up "surfeited, disgusted, bored," is British slang first recorded 1900, extended to U.S. by World War I; probably from earlier phrases like fed up to the back teeth.
1788, short for Federalist; as colloquial for "official of the federal government," from 1916, especially, after 1930s, of FBI agents.
Old English fedan "nourish, feed, sustain, foster," from Proto-Germanic *fodjan (cf. Old Saxon fodjan, Old Frisian feda, Dutch voeden, Old High German fuotan, Old Norse foeða, Gothic fodjan "to feed"), from PIE *pa- "to protect, feed" (see food). Feeding frenzy is from 1989, metaphoric extension of a phrase that had been used of sharks since 1950s.
"action of feeding," 1570s, from feed (v.). Meaning "food for animals" is first attested 1580s. Of machinery, from 1892.
Any federal government worker or agent, esp in law enforcement or taxation: right up to the day the Feds dragged him into court (1912+)