Nope. She's tall for her age and actually that's how much I way and I'm 13 too except I'm 5'8". She's fine but if you really are concerned for her weight just make sure you remind her in little gentle ways. Like I know a friend who has a ring that says Don't. It reminds her to eat better when she's reaching for a cookie or junk food. Just make sure she's exercising and invite her on a jog or play tag with some friends. Help keep her active and show her that good foods can be delicious too! Every little thing counts but if she's comfortable with her body then there's really no need to change her unless she's morbidly obess.
She's perfectly fine. If you are really concerned, consult the charts medical professionals use to compare height and weight to the average. But be aware that standards vary by country. Some kids also just grow faster in different areas than others
Also, media has a big say in this. Back in the day, the more curves you had the better- it was considered a sign of health and even wealth
Her BMI is in the normal range. Of course, she is only 13; so she will grow & change as she matures. (: Exercise & eating healthy are a good habits for your sis to start forming now. And if she doesn't like how she feels/looks, then she can always lose some weight. I don't think she really needs to though. P.S. Always make sure your sis knows she's beautiful, no matter what. (: And you're a good sister, trying to help your sister out. (: