Green’s Dictionary of Slang

1. (US) an idiot, a fool.

1919		DN V 61: Cheese-head, a green, awkward person.
1923		St Louis Star (MO) 22 Feb. 8/4: ‘We’re not through with you — you little cheese-head [...] Just think it over [...] and get the blubber out of that ivory dome of yours’.
1939		R. Chandler Big Sleep 83: My God [...] You let this cheese-head sit there and insult me, Joe?
1940		L.A. Times Sun. Mag. 11 Feb. 8/1: The sidewalk Romeos started after her [...] each thinking what a cheesehead he’d been to disregard the attractions of Hattie McDonald.
1960, 1975		Wentworth & Flexner DAS.
1985		T.R. Houser Central Sl. 14: cheese head A person for whom one has scorn or contempt.
1989		H. Rawson Dict. of Invective (1991) 77: cheesehead (a dullard).

2. (US teen) a general pej. term, esp. directed at an overly emotional or dramatic person.

2002

D.H. Sterry Chicken (2003) 175: Change the record, Cheesehead.