1831, "heavyweight horseman," later "boxer or wrestler of a certain weight" (1896), from earlier welter "heavyweight horseman or boxer" (1804), possibly from welt (v.) "beat severely" (c. 1400).
... but at the end of the first German mile, Nature gave way, and this excellent mare was obliged to "knock under" to the extraordinary exertions she had made, and to the welter weight she carried, upwards of 13 stone. [The Sporting Magazine, September 1831]
as in the real McCoy, "the real thing; the genuine article," by 1881, said to be from Scottish the real Mackay (1883), which is of uncertain origin, though there are many candidates, the most likely of which is that it refers to whiskey distilled by A. and M. Mackay of Glasgow (the phrase the real McCoy became popular during Prohibition to describe liquor). Other stories credit it to Charles S. "Kid" McCoy (1872-1940), former welterweight boxing champ; and to a claimant for chief of the northern branch of the clan Mackay.
"By jingo! yes; so it will be. It's the 'real McCoy,' as Jim Hicks says. Nobody but a devil can find us there." [James S. Bond, "The Rise and Fall of the Union Club," Yorkville, Canada, 1881]