Oh, this is very difficult. You have the proper mindset. You genuinely care. And there is not A THING you can do that will make it better.
You have mirrors in your house. She sees her body. She feels guilt and the more guilt she feels, the more she eats to calm the guilt. So there is nothing you can SAY. And yes, if you do talk about her weight ,it will trigger her insecurity (we woman are all insecure about our bodies until we get so old that we finally understand that once we were pretty). Trigger her insecurity AND her fear that ALL you care about is not her, but how she looks. And that will drive a very subtle wedge between you and her ... both emotionally and sexually too, since female sexuality is highly-dependent on our emotional state.
What you CAN do is act as if she still turns you on. AND start doing active things that you invite her to join you on ... even something as simple as a half-hour walk after supper ... hand-in-hand, building companionship together (as well as the secret agenda of increasing her activity level). More active sports too if you can get her involved. Take up camping and the two of you can go hiking around the nature areas. Going on bicycle picnics. Whatever.
Lastly, women who are unhappy overeat. And gain weight. I don't know why she is unhappy. It may have nothing to do with you. It may have to do with unrealistic ideas about relationships (the "happy-ever-after" always fades out and leave people dissatisfied and disillusioned ). Or it may have to do with buried issues from her childhood. Or YOU may be contributing to disappointment or buried anger in some way. I do not know, I cannot know.
So try as best you can to be more romantic, nurturing and approving of her - flaws and all NO relationship lasts for long unless we CAN accept our partner flaws and all. Even if you have nothing to do with her discontent, your affection, company, and love can help ease it. As long as you don't overdo it so that it seems insincere.
And work on the communication. Things can simmer and rot underneath the surface if there is not good communication. It may be that this is triggering her discontent. And if the communication is not very good between you two, then perhaps couples therapy could help (that is what it is for .. not for pointing fingers, but for learning the couple how to communicate better).
The problem is that you cannot do this for her. And you cannot motivate her either, without risking serious repercussions for you and for your relationship with her. The best you can do is subtly get her to exercise with you, give her more acceptance and affection. And hope that SHE can figure out how to work with whatever is bothering her.