Your dh sounds like such a lovely person op. Maybe he has taken too much on? Can you help lighten his load a little by taking on some more of his domestic chores? (Which is what I would say to a man who was complaining about his wife putting on weight and not taking care of herself.) How much time does he get to rest and de-stress? Do you each get the same time to decompress?
Also, what is his diet and sleep quality like? Does he get time to exercise? Helping him to focus on those three things might be beneficial?
Could you very gently mention that you are concerned about his health and perhaps you could agree on a healthy eating plan together?
You are quite wrong about depression by the way way. It is perfectly possible to be going to work and completing all of your activities while feeling deep inward despair and bleakness.
High-functioning depression, also known as "functioning depression," describes individuals who experience symptoms of depression but are still able to maintain their daily routines and responsibilities, such as working and managing relationships. While they may appear to be coping well externally, they may be struggling with significant emotional distress and negative feelings internally. It's not an official diagnosis in the DSM-5, but it's a term used to describe this specific experience of depression.
You should encourage him to seek treatment.
That would be my first step, As depression and stress can cause you to have high cortisol levels which can make it harder to lose weight.
In fact, why aren’t you posting on here about your difficulties in communication? Your sex life won’t improve unless you can talk to one another. Maybe he is depressed about your relationship as you do sound quite cold op. It sounds as if there is far more to this than you have posted. . Problems in the bedroom are usually a symptom of some other fundamental difficulty in a marriage.
Ultimately, he needs to feel good about himself and project confidence in order for you to find him attractive. So be careful not to crush his self esteem further when addressing this. The best way would be to frame it in terms of concern for his physical and mental health.
I hope that doesn’t sound too harsh op. It’s far from easy trying to talk to someone who withdraws and becomes upset and tearful and won’t take action to help themselves. It sounds like he needs an urgent trip to the gp and a therapist and maybe you need marriage counselling when he is feeling more like himself.
As a start, maybe you could offer to go out in the sunshine and walk with him every day as walking has been proven to be effective for mild depression, but he might need meds to really resolve it. Walking can’t harm him anyway.
Whatever you do, don’t stay with him just for the financial stability op, That would be soul-destroying for both of you. if there is no love or kindness left between you, then do the decent thing and make a clean break.