Late 19th century: corruption of what cheer?.

• cheer from Middle English:

  In medieval English the word cheer meant ‘face’, coming ultimately from Greek kara ‘head’. People came to use it to refer to the expression on someone's face, and hence to their mood or demeanour. This could be in either a positive or negative sense; you could talk, for example, about a person's ‘sorrowful cheer’ or ‘heavy cheer’. ‘What cheer?’ was once a common greeting meaning ‘how are you?’, and in the 19th century this eventually became worn down to wotcha. Over time cheer developed the specific meaning of ‘a good mood’ and then ‘a shout of encouragement or joy’. A Bronx cheer is a rude noise made by blowing through closed lips with the tongue between them—what is also called a raspberry.

1920s: contraction.