c. 1500, "old or decayed tree stump" (Douglas), a provincial word of unknown origin. The meaning was extended to "small ox or cow," especially of the breeds characteristic of Wales and the Scottish Highlands (1540s, if indeed this is the same word), and by 1610s generally to undersized animals and ignorant people.
The slang sense of "person of low but thick-set build; a stocky, stunted person," a term of abuse, is by 1700. The sense of "smallest of a litter" (especially of pigs) is attested from 1841 as a Shropshire word, though it seems to have become general in American English. Some see a connection of runt, at least in the "animal" sense, to Middle Dutch runt "ox," but OED thinks this unlikely, and pronounces the word "of obscure origin." Related: Runty (1807); runtish (1640s).