The Centers for Disease Control and Prevention reports that the normal weight of a 13-year-old girl varies dramatically based on her growth curve and height, making it impossible to dictate a weight that is "normal" for every teen. Each child grows on his or her own growth curve; pediatricians use the curve to help evaluate the healthiness of a teen's weight.
Even if a 13-year-old girl reaches a weight that is high for her growth curve, this does not mean she is overweight. It is possible that a growth spurt is going to follow this increase in weight, making her new weight normal for her height.
A normal weight also varies based on the teen's body composition. A teen may weigh more than a peer due to having a large amount of muscle.