mid-14c., "short or insufficient in quantity, rather less than is wanted for the purpose," from a Scandinavian source such as Old Norse skamt, neuter of skammr "short, brief," from Proto-Germanic *skamma- (source also of Old English scamm "short," Old High German skemmen "to shorten"), perhaps ultimately "hornless" (from PIE *kem- (1) "hornless;" see hind (n.)).
Also in Middle English as a noun, "dearth, scant supply, scarcity," from Old Norse.
mid-15c., scanten, "be deficient, fail," also "be sparing," from scant (adj.). From 1560s as "put on scant allowance, limit;" 1580s as "make small or scanty, diminish." The meaning "treat slightingly" is by c. 1600. As an adverb, "scarcely, hardly," by mid-15c.