cry for something—
1. weep in order to get food, attention, etc.:
- While the rescuers were still clearing the debris, the child was crying for water.
2. need smth. very much:
- It’s a reversal from problems felt earlier this summer when the region was crying for rain amid a drought.
cry out for something— = cry for something 2:
- Over decades, Jackie has been one of the women crying out for support in stopping the violence.