"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"]
-ness
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).