Unknown, but lexicographer Eric Partridge (1894-1976) speculated that it may be a corruption of cease.
In his Vocabulary of the Flash Language, author and former convict James Hardy Vaux (1782-?) defined cheese it as synonymous with stash it and stow it, all meaning to desist or leave off.
- (idiomatic, slang) An imperative used as a warning to stop, hide, or flee
1960, P. G. Wodehouse, Jeeves in the Offing, chapter VIII:
- Knowing that Bobbie would be on sentry-go made all the difference. Any gangster will tell you that the strain and anxiety of busting a safe are greatly diminished if you've a look-out man ready at any moment to say “Cheese it, the cops!”
a warning to stop, hide, or flee