What you said was the equivalent of punching someone in the face. A simple apology is not sufficient to make up for it. I'm sorry to make that analogy, but I grew up with a person who struggled with his weight and I believe that's how he felt when people commented on it.
If you really want to rebuild your relationship with this person, you should tell her that you have problems communicating and really didn't understand how hurtful your comment was. You could give an example of another time that you made a mistake like this. Then ask if she could consider giving you another chance, because her friendship is important to you.
Even then she might not be able to get over it, and she would be entitled to feel that way.