half-wit (n.)

"simpleton" (one lacking all his wits), 1755, from half + wit (n.). Earlier "a would-be wit whose abilities are mediocre" (1670s).

Half-wits are fleas; so little and so light,

We scarce could know they live, but that they bite.

[Dryden, "All for Love"]

Phrase out of half wit "half out of one's mind" was in Middle English (late 14c.). Half-witted "lacking common sense" is from 1640s.