You have a few choices, all of them bad if your wife does not respond favorably.
You can divorce over this.
You can accept a sexless marriage.
You can pester her for sex.
You can cheat.
I know you don't like any of them. You want "stay married and have mutually satisfying sex". For now, that is not on your menu.
I like this, very well put. Cheating is not an option for me. I may not be a perfect person, but I know in my heart I am not a person who could ever cheat on their spouse. Even if I do end up very successful in my weight loss goal and end up attracting other women, I will not cheat. I could never be THAT GUY. Even if she cheats on me, I wouldn't have a revenge affair. I would just end it. When we were younger and other women would come on to me, I used to take great pleasure in shooting them down and making them feel stupid for trying, because I already have a great woman. And she still is a great woman.
Divorce is not something I wish to do, nor does she. We've worked hard to build a life together, and that's not something I take for granted. We still have a lot of goals that we want to accomplish together. The only way I'd consider divorce is if she cheated on me, or just went off the reservation crazy. I am pretty confident that neither scenario will happen, but not naive enough to discount it completely. At the end of the day, you can really only control your own actions.
I am going to stop pestering for sex. I might ask if she wants to periodically, and if the answer is no, I'll just suck it up, take it like a man and go jerk off. I haven't even asked for sex in over 2 weeks. She has initiated once, I agreed, and it was your standard duty sex. I don't even know why she initiated, since she clearly wasn't in the mood. I think she just thought she should check it off the to do list. But in the future, if she initiates and I can tell she's just doing it out of a sense of obligation, I will pass.
As you said, no sex IS better than duty sex. I can deal with no sex, honestly. If sex were taken completely off the table, I could accept that and just get on with my life. But this wondering "why isn't she into it? Is it something I'm doing wrong? WHAT WOMAN, WHAT??!!" is annoying, and quite frankly it's affecting my mental well being. It sometimes makes me an *******. I suppose part of that logic is that if there is NO sex, then it's clearly HER problem. But if there's occasion passionless, emotionless duty or starfish sex, then it could also be MY problem. It could be something I'M not doing right.
It's sad and a little bit frustrating. It really bothers me that some guys can act like complete *******s, even CHEAT on their wives, and the result is that their women can't get enough of them. I think that's the part that hurts the most.