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.
"cheese-it." YourDictionary, n.d. Web. 24 May 2018. <http://www.yourdictionary.com/cheese-it>.
cheese-it. (n.d.). Retrieved May 24th, 2018, from http://www.yourdictionary.com/cheese-it