fed (n.) Look up fed at Dictionary.com
1788, short for Federalist; as colloquial for "official of the federal government," from 1916; especially, since 1930s, of FBI agents.
fed (adj.) Look up fed at Dictionary.com
past participle adjective from feed (v.). Fed up "surfeited, disgusted, bored," is British slang first recorded 1900 (some early uses connect it to the Boer War), extended to U.S. by World War I; probably from earlier phrases like fed up to the back teeth. Earlier it was used of livestock, "fatten up by feeding." The notion probably is the same one in to have had enough "to have had too much."