What is the origin and meaning of the term 'Chubby Chubs'?

Solution 1:

Etymonline has an entry for chubby meaning "like or resembling a chub". A chub is a type of fish, notably short, thick and stocky. It cites its appearance as in 1610, following chub being applied to people around 1560.

Chubby-chub is an alliterative/reduplicative term of endearment for someone who is similarly stocky.

I haven't heard "chubby-chub" very much; chubby-chops (meaning "plump-cheeked") appears more often in British English.

Solution 2:

Chubby

The OED has the adjective chubby, meaning short and thick like the river fish called chub, from 1611, but notes it is obsolete. Meaning round-faced or plump and well-rounded, they have it from 1722. For combinations, they have chubby-faced from 1826 and chubby-headed from 1884.

Chubbed, meaning big headed like a chub, is from 1674. Chub-cheeked, having chubby cheeks or face, is obsolete and from 1715. Likewise, chub-faced is obsolete and from 1602. Chub-headed is 1796.

Chubby chops

Searching Google Books, I found Chubby-chops in the 1769 The History And Adventures Of An Atom by Tobias Smollett, as a translation of the Italian name Gozzi:

Porcinas Giudices itsColonnas Mura torios Medicis and Gozzi Endea vours Chuckle heads Black Muzzles Hogs Judges Pillars Masons Leeches and Chubby chops

You may remember an Italian minister called Grossa-testa, or Great-head, though in fact he had scarce any head at all. That nation has, likewise, its Sforzas, Malatestas, Boccanigras, Porcinas, Guidices; its Colonnas, Muratorios, Medices, and Gozzi; Endeavours, Chuckle-heads, Black Muzzles, Hogs, Judges, Pillars, Masons, Leeches and Chubby-chops.

A few pages earlier it uses Chubby-cheeks as a translation of the Roman name Malici:

What need I mention the Plauti, Panci, Valgi, Vari, Vatiæ, and Scauri; the Tuditani, the Malici, Cenestellœ and Leccœ; in other words the Splay-foots, Bandy legs, Shamble-shins, Baker-knees, Club-foots, Hammer-heads, Chubby-cheeks, Bald-heads and Letchers ... yet all those were great families in Rome.

Chubby chubs

This is a much later variation. The earliest I found via Google Books is Rootabaga Stories (1922) by American author Carl Sandburg, in "The Wedding Procession of the Rag Doll and the Broom Handle and Who Was in It":

The Chubby Chubs were next. They were roly poly, round faced smackers and snoozers. They were not fat babies—oh no, oh no—not fat but just chubby and easy to squeeze. They marched on their chubby legs and chubby feet and chubbed their chubbs and looked around and chubbed their chubbs again.