Perhaps your success is reminding her that she hasn't had any. That can lead to resentment.

In regards to the weight...yes, she'll have to have the motivation to lose weight. I suspect you've suggested this already, but perhaps you could both go to a gym together. Or go for walks together once the weather is better (I don't know...is it better where you are already? I'm looking at 4 ft snow drifts outside of my office window at the moment). Just anything really to get more active. When people are more active, it becomes easier to just get out and do more things.

One more thing...just because she is seemingly willing to work at this relationship now, doesn't mean you have to. It will take a lot of soul searching on your part, but perhaps you don't want to be in the situation any longer. If you don't honestly think you can be happy and really don't see things changing, you might need to make the decision. You are not responsible for her happiness - she is. If she can't be happy, that's not your fault, Adam.