MAKE WEIGHT. A small candle: a term applied to a little slender man. [Grose, "Dictionary of the Vulgar Tongue," London, 1785]
For the formation, compare makeshift, also make-sport (1610s), makegame (1762) "a laughing stock, a butt for jokes;" makebate "one who excites contentions and quarrels" (1520s); makepeace "a peace-maker, one who reconciles persons at variance" (early 13c. as a surname).