"fat, round, and plump," 1610s, literally "resembling a chub," from chub, the short, thick type of fish + -y (2). Perhaps influenced by Old Norse kumba "log," kumben "stumpy."
ME chubbe ... was also used of a "lazy, spiritless fellow; a rustic, simpleton; dolt, fool" (1558), whilst Bailey has "Chub, a Jolt-head, a great-headed, full-cheeked Fellow," a description reminiscent of that of the chevin, another name for the chub ... Thus the nickname may have meant either "short and thick, dumpy like a chub," or "of the nature of a chub, dull and clownish." ["Dictionary of English Surnames"]