" Weep" is not used in everyday language. One would hear " cry" a lot more often, even daily. Here are two examples. I hope they help. I would weep if someone close to me died. (Mourn;grieve;sob) I would cry if I broke a bone in my body. (Expressing physical pain or mild emotions such as happiness even) I will cry at my wedding. A baby will cry when he/she is hungry. I will weep when my mother dies. The use of cry is almost always correct, understood, and accepted.

Cry can be with or without vocalizing, weep is without vocalizing, only tears.