You are totally right to request from them to work. But it is also reasonable that they don’t want to be seen as fat.

You are partners and you should empathize for each other. Meaning you should find a middle ground to solve this.

My recommendation is to set a deadline for them to lose weight and also it would be supportive for them if you also join the diet(if you don’t need to lose weight, a diet focuses more on healthy eating) with them.

You are not the asshole for sure, but also don’t forget you both are partners, should be caring for each other. I am saying this because this struggle may damage your relationship real bad, just try to find middle ground.