"short, thick piece" of something, 1690s, probably a nasalized variant of chuck (n.1) "cut of meat;" meaning "large amount" is 1883, American English. Meaning "person or beast that is small but thick-set and strong" is from 1822.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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Harper, D. (n.d.). Etymology of chunky. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/chunky