First of all, don't go assuming she is sick or absent because of her weight. You're no doctor and, even if you are, you didn't mention that you're her doctor. There are a lot of 'overweight' people in the workplace that are healthy and never miss work. There are also a lot of 'thin' people that call in sick every other week.
So, take off the stethoscope and white coat and get down to the issue you should be talking to her about. That's her absenteeism. Have the absenteeism data in front of you when you sit down with her. Start the conversation with, "Debby, you are a very valuable person and you contribute a lot to the team when you're here, but you aren't here enough. That's causing a hardship for the rest of the team and has to change, so let's talk about that."
Your role and responsibility is to ask questions, listen to her answers, help her problem solve, offer her resources (like human resources or the employee assistance program) if they are needed, and to remember that it is her responsibility to figure out how to be at work enough to do her job.
If, over time, she can't do it, then you have to start using your internal support systems (human resources and legal) to help her transition out to a job she can physically handle.
Karen