The quality or state of being chubby; the condition of having a rounded, plump body.
From 'chubby' (of obscure origin, possibly from Old English 'chub' referring to the fish) plus the suffix '-edness' which turns adjectives into nouns describing their qualities.
The word 'chub' originally referred to a round freshwater fish, and people probably called chubby humans 'chubby' because they resembled these plump fish! This shows how animal names often jump to human descriptions.
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