"quietly sullen," 1744, of uncertain origin. Connection has been suggested to obsolete, rare sulke "hard to sell" (1630s) and to Old English asolcen "idle, lazy, slow," past-participle adjective from aseolcan "become sluggish, be weak or idle" (related to besylcan "be languid"), from Proto-Germanic *seklan (source also of Middle High German selken "to drop, fall"). But words of similar meaning often are held to be imitative (compare miff, mope, boudoir). Related: Sulkily; sulkiness.
"light carriage with two wheels," 1756, apparently a noun use of sulky (adj.), on notion of "standoffishness," because the carriage has room for only one person and obliges the rider to be alone.