Discharged from an obligation, “acquitted.”
To John I owed great obligation; But John unhappily thought fit To publish it to all the nation- Now I and John are fairly quit.
Cry quits. When two boys quarrel, and one has had enough, he says, “Cry quits,” meaning, “Let us leave off, and call it a drawn game.” So in an unequal distribution, he who has the largest share restores a portion and “cries quits,” meaning that he has made the distribution equal. Here quit means “acquittal” or discharge.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894