c. 1300, "to fall (into water) or strike with a full impact," a common Low German word, from or related to Middle Dutch and Dutch plompen, East Frisian plumpen, Middle Low German plumpen, probably more or less imitative of something hard striking something soft. Perhaps influenced by or merged with Middle English plumben "immerse (in liquid)," late 14c., from plumb (n.) in the "weight" sense. Hence plump (n.) "a firm blow," in pugilism usually one to the belly.
To plump; to strike, or shoot. I'll give you a plump in the bread basket, or the victualling office; I'll give you a blow in the stomach. [Grose, "Dictionary of the Vulgar Tongue," London, 1785]
Or, even if any of them should suspect me, I know how to bring myself off. It is but pretending to be affronted, stripping directly, challenging him to fight, and before he can be on his guard, hitting him a plump in the bread-basket, that shall make him throw up his accounts; and I'll engage he will have but very little stomach to accuse me after. ["The Reverie: or A Flight to the Paradise of Fools," London, 1763]
As an adverb, "at once," as in a sudden fall, from 1590s.