From Middle English daf, daffe, from Old Norse daufr ("deaf, stupid"), from Proto-Germanic *daubaz ("deaf, stunned"), from Proto-Indo-European *dʰewbʰ- ("to whisk, whirl, smoke, be obscure"). dowf, and dof. Cognate with Swedish döv ("deaf"), Danish døv ("deaf, stupid"). More at deaf.
From Middle English daffen ("to render foolish"), from daf, daffe. See above.