I tried to look it up: These depictions began to appear during the Edo era (1603-1868) and, as far as I can tell, it's not entirely known why they had these gargantuan ballsacks.

Their skin, used by artisans, was known for it's great elasticity. In Japanese folklore, the tanuki are capable of shapeshifting.

In Japan today, tanuki statues are often placed outside establishments such as restaurants, and are said to bring good fortune.

Real raccoons do not have enormous balls.

TLN: ~~keikaku means plan~~ Tanuki means raccoon