Hi, I understand that u feel kind of bewildered by your gf thoughts... Personally, i think that sex is important in a relationship but it's not the whole thing.Sex is part of the relationship and the ultimate thing to express your feelings to your significant other, this is why it's so important. You point out that u are overweight and this kind of complicates things. What if you talk with your gf so she becomes supportive with u on a diet plan or such? I am overweight also(very much at the moment), but I have had sex anyways. Tell your gf that there are many ways to enjoy sex

and talk about it next time with her when u become intimate.

I see that at the moment you feel kind of bad with yourself, but you don't have anything that is incurable

... Ask your gf for some more support and help and let her know that u feel a little hurt by what she said. I don't understand why you can't have sex just because you are overweight.
Also, I sense a little fear in your words since u mention that your gf talks with her x-bf. Maybe right now u feel susceptible, but maybe you should talk with her also on that subject.
Being overweight is not fun, I know, but it's worse when the other person that you love doesn't support you. And believe me, there are many ways to enjoy sex!

My best wishes, Rappaccini