"thigh of a hog used for food" (especially salted and cured or smoke-dried), 1630s, extended from earlier sense " part of the human leg behind the knee; hock of a quadruped," from Old English hamm "hollow or bend of the knee," from Proto-Germanic *hamma- (source also of Old Norse höm, Middle Low German, Middle Dutch hamme, Old High German hamma), from PIE *kone-mo- "shin bone" (source also of Greek kneme "calf of the leg," Old Irish cnaim "bone"). Ham-fisted (adj.) in reference to hard-hitting characters is from 1905; ham-handed "coarse, clumsy" is by 1896. With hammen ifalden "with folded hams" was a Middle English way of saying "kneeling."
"overacting inferior performer," 1882, American English, apparently a shortening of hamfatter (1880) "actor of low grade," which is said (at least since 1889) to be from the old minstrel show song, "The Ham-fat Man" (attested by 1856). The song, a comical black-face number, has nothing to do with acting, but the connection might be with the quality of acting in minstrel shows, where the song was popular (compare the definition of hambone in the 1942 "American Thesaurus of Slang," "unconvincing blackface dialectician"). Its most popular aspect was the chorus and the performance of the line "Hoochee, kouchee, kouchee, says the ham fat man."
Ham also had a sports slang sense of "incompetent pugilist" (1888), perhaps from the notion in ham-fisted. The notion of "amateurish" led to the sense of "amateur radio operator" (1919).
"over-act in performance," 1933, from ham (n.2). Related: Hammed; hamming. As an adjective in this sense by 1935.