Not only do women generally really care about their appearance, we also live in a superficial appearence obsessed society.
Insta, billboards, TV all of that contributes to women's insecurity and constant preoccupation with their bodies.
The average woman stresses about her weight and a lot of women around me, even the obese ones are constantly trying to diet. Some just don't know the right way of going about it or are going through depression ect, which makes it even harder to shift the weight.
My point is, I highly doubt the wife doesn't want to lose weight. A lot more is probably going on that you are omitting or I wouldn't even be suprised if the husband even isn't aware.