The first reference to ``cheesy'' in this context in my OED is from a book called Student Slang by a Gore in 1896, but I'm having a hard time finding any more reference to that, so I can't tell if he was American or English. However, the second reference is from a P.G. Wodehouse Jeeves novel written 34 years later, who was an Englishman living in America, so that doesn't help any more. (Boy, that was all helpful, wasn't it?)

Regardless, yes -- we do know that meaning.