The last thing you want to do is tell the truth. No doubt she is capable of looking in a mirror, and she is already well aware of her weight issue. It doesn't matter if you say "get lost fatty," or "sweetie, I feel really sorry to say this, but I just can't continue our relationship with your health issue," the result of both of these will be the same. Even if you don't mention her weight at all, she will probably assume that is the reason you are leaving her. All obese people tend to have self-esteem issues, I can't think of one person that is happy being fat.
My advice would be to see her less and less. It will make it easier when you breakup. Get it to the point where you only see each other every few weeks at most. Make up some excuse depending on your situation ... more hours at work, taking another class at school, taking care of sick grandma ... whatever as long as it is plausible.
If you do this right over a period of a month or so then you will quickly get to the point where "I think we should see other people" is a lot easier to say because you will have already had a defacto breakup by spending so little time together.
That is the best way I can think of to let her down gently without devastating her. A lot less stress for both parties. Honesty is not a good idea in this case.
