Green’s Dictionary of Slang

to collapse in the face of pressure and act like a weeping, pleading child; also in fig. use.

1902		O. Wister Virginian 85: I am not crybabying to the judge.
1932		(con. 1919) Dos Passos Nineteen Nineteen in USA (1966) 644: Now they try to crybaby and say they wanted peace all along.