Not a medical term. Medically speaking, there is no such thing as a "weak uterus." sometimes, people refer to a "weak uterus" when a woman has repeated miscarriages or has a condition called incompetent cervix (more appropriately called cervical insufficiency) that may lead to a late miscarriage.
Incompetent cx. If you have this, your doctor should have fully explained it to you already. It is where the cervix opens up too soon, anytime usually after 16 weeks and you lose the pregnancy. It can be diagnosed by an ultrasound before it happens and if you do have incompetent cx., a stitch can be placed by a competent obgyn to keep teh cervix closed and you will have to modify your activity and be monitored.
Weak uterus. Weak uterus may be used as a lay term for prolapsed uterus (uterus sinks into vaginal canal). A weak cervix is a different issue.
Cervical incompetenc. Probably talking about cervical incompetence.