How did the slang phrase "Cheese it!" come to be?

cheese It
Stop, look out, as in Cheese it! Here come the cops! This term, generally stated as an imperative, may have been a replacement for the earlier "Stop at once." Eric Partridge speculated that it may have been a corruption of Cease! but its true origin is not known. [Slang; mid-1800s]

https://idioms.thefreedictionary.com/cheese+it

The actual fixed idiom here is simply "cheese it' (because that part of the phrase can be used alone and still keep the same meaning), so we'll leave "the cops' out of this explanation. "Cheese it' has been part of English slang since at least the mid-1800s. The word "cheese' has been used with the meaning "to put an end to' or "to stop' since at least 1812, and this is the sense which led to the idiomatic expression. Whoever began using "cheese' in that way apparently decided to "cheese it' when people asked why, though, because no one has ever determined where that sense came from or why putting an end to an action should be related to cheese. The exact origin of the phrase must be labeled unknown.



http://www.jewishworldreview.com/0304/dictionary_men.asp