Do not ever have duty sex. Do not ever have quickies. Any more. Every again. If you start to have sex and you can see she isn't aroused and isn't interested, stop, get dressed and tell her many another time when she's into it. That's all. No more.
While it's not entirely her job to come to the table ready to be penetrated, it is her job to come to the table ready to be aroused.
I don't agree with never, but I do think that if that is the only kind of sex you both are having its not a good thing for the marriage.
If my husband could have heard the mind play going through my head most of the time we had duty (or pity sex), I am pretty sure he would have been horrified and would never have accepted pity sex again. I don't know what is going on in your wife's head, but I hope for your sake, and even more so for your wife's sake it is no where near what was in my head. It was not loving thoughts, that's for sure.
May I suggest you try an experiment. For the next month, don't initiate sex, but do initiate cuddling sessions. If you get aroused, which can't be helped, DON'T ACT on it in anyway, like rub up against her. Simply hold her and tell her she is beautiful and why you love her, etc. If she initiates sex, tell her you appreciate it, but you want what little intimate time you have to be enjoyable for the both of you. Then offer her a back rub or foot rub, or hot bath. If she chooses a hot bath, bathe her, wash her hair. Think non sexual sensual touch. Treat her like a queen during these intimate times. Stay with her, be with her emotionally and physically, just not sexually UNLESS you are SURE she is aroused and wants sex for herself not just for you. Then report back here after the month.
In the mean time, take care of yourself so you are not grouchy and horny. BUT NO PORN. Think of her to get off. And do work on your weight, for the both of you. That's always a good idea. Don't be needy, dont be a puppy dog looking for attention the rest of the time. Just enjoy being a man, a husband, a father, and her boyfriend for this month period and see what happens.