"worthless sponging idler," 1863, American English slang, perhaps originally Civil War slang, from dead (adj.) + beat. Earlier used colloquially as an adjectival expression to mean "completely beaten" (1821), and perhaps the base notion is of "worn out, good for nothing." It is noted in a British source from 1861 as a term for "a pensioner."
In England "dead beat" means worn out, used up. ... But here, "dead beat" is used, as a substantive, to mean a scoundrel, a shiftless, swindling vagabond. We hear it said that such a man is a beat or a dead beat. The phrase thus used is not even good slang. It is neither humorous nor descriptive. There is not in it even a perversion of the sense of the words of which it is composed. Its origin is quite beyond conjecture. ["Americanisms," in "The Galaxy," January 1878]It also was used of a kind of regulating mechanism in pendulum clocks.
Completely exhausted: My poor ass is draggin' and I'm dead beat (1821+)
To sponge, loaf, etc: Living off interest is not exactly deadbeating
[1863+; fr dead, ''complete, completely'' and beat, ''sponger'']