The online etymological dictionary gives us: whopper (n.)
1767, "uncommonly large thing," originally and especially an audacious lie, formed as if from whop (v.) "to beat, overcome." Whopping "large, big, impressive" is attested by 1620s.

also from 1767
whop (v.)
"to beat, strike," mid-15c., of imitative origin. Compare Welsh chwap "a stroke," also of imitative origin; also see wap. Related: Whopped; whopping.
So yes, the association with bloated bodies may be fakelore, but you never know. The words still sound the same.