Yes, these words are synonyms. Still, most people will experience a shade of meaning between cry and weep, even if they're not aware of it.
Weeping is associated with grief, mourning and profound sadness of some kind. It's an internal state expressed through tears. Weeping is of the soul.
Crying is an exhibition of a more shallow and fleeting emotional reaction. You can cry angry tears, for instance. I wouldn't use weep to describe a child throwing a tantrum unless I was trying to be funny. If I've had a big day that ended in tears, cry with frustration describes this state better than weep.
02.10.2018 ob 16:45