Like you said, it is pretty much of a no win situation for the H. I think you need not to try and convince her. She doesn't feel good about herself. All you can do is compliment her. If you over kill.......she'll tune it out. She wants to hear someone who is unbiased tell her she looks good. I've heard some women make the statement about their H, "Well, he has to say I look good". Which, I think they mean he is biased b/c he loves her. It's like when a stranger gives you a compliment, or you run into an old classmate and they say you haven't aged......it makes you feel good.
I don't mean to sound as if a W doesn't want her H's compliments, however, we know the H sees through eyes of love.......which means (to many women) that the H would naturally say she looks fine. On the other hand, it's a minefield b/c if he sounds as if he is suggesting, or agrees, she should lose weight.......then she gets an attitude toward him.
Just listen when she talks. If she asks what you think, say something like, "I think you are beautiful just as you are, but if you don't feel good about yourself, and if you want to do something.....I'll support it, as long as it's healthy".
Have you thought about inviting her to go workout at at the gym with you? That could be a shared activity.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!