Green’s Dictionary of Slang

foolish, stupid.

1949		S.J. Perelman letter 20 Apr. in Crowther Don’t Tread on Me (1987) 95: I have come away with the most vitriolic loathing of these cheese-headed bastards.
1995		J. Stahl Permanent Midnight 72: My wife had landed a slot as a D-girl [...] for yet another cheesehead producer.