Green’s Dictionary of Slang

fine or showy.

1855		Delhi Sketch Bk 1 Oct. 120/1: [H]e says they [i.e. cricketing flannels] are superior (cheesey I think was his expression) and fashionable at Lord’s.
1858		R.S. Surtees Ask Mamma 266: His cheesy hat well down on his nose, with his stout, well-cleaned doe-skin gloves.
1859, 1860		Hotten Dict. of Modern Sl. etc.
1866		Letters by an Odd Boy 49: A live cat, with her tail for a handle, waas considered very cheesy.
1873		Sl. Dict.
1997		Sun. Indep. (Dublin) Living & Leisure 1 June 11L/2: Men imagining that deeply tanned, cheesy, muscled blokes are sexy.