Maybe the weight is the most noticeable thing to you but overeating etc is probably replacing dopamine that she's not getting elsewhere. Obesity is very complex, and can be caused by lots of things. Once you're there it's very difficult to lose weight because a bunch of changes can introduce a cascade of factors that make it even harder e.g. feeling more hungry due to nutrient deficiencies, loss of muscle mass and difficulty moving, fatigue, hormones. Def encourage her to see a therapist and avoid trying to get her to eat less. If there's anything you can do to lessen her burden, e.g. cooking a healthy meal for both of you, that will kickstart the nutrient side of things and help a bit with lessening her mental load. Building a shared enjoyment of physical activity (not like intense exercise to lose weight) will help you guys schedule some down time together (and a surprisingly low amount is necessary, like 2.5 hrs of moderate intensity exercise per week). Maybe leave the gym idea and ask if she wants to come for a walk with you while you guys chat about the week. The benefits of exercise healthwise are enormous for people who previously did no exercise but start doing low amounts of incidental exercise. You could also join her for a bit of TV occasionally in the evenings to reconnect and vegetate a bit after a tough day.