Wife’s depression

She needs counselling from a professional psychologist - a real one. Cognitive-Behavioural Therapy might help against those food binges and also with self-esteem.
She can do gym at home! Motivation/boredom trouble with exercise?
Put easy dance-teaching videos on... make it a fun experience for both of you!
Weight has never been a problem in a friendship - why is she away from her friends?
If her friendships are not healthy..... maybe she needs to make new friends?
Take the extra mile to take her out often around people and make her feel cared for - the prettiest lady around - you can do that to help her confidence. Body image problems - hit the gym together, many times - these classes involving movement could help her motivation especially if she feels lonely. She seems to have been static for long - she needs to begin feeling joy from movement again - so you can start light and build on with longer sessions and more exercises later on. Also, cook new healthier things together - organize and try new stuff (better than binging on junk food). Invest her in new things (get a babysitter if you have to) - if she has something distracting her from her own self-destructive thoughts, she may even begin discovering new skills and strengths which will empower her to have growing thoughts instead of self -diminishing ones. She is more than her body shape BUT if it affects her psychological and physical health - she must take action.

Some words for anion who feels down and overweight and or with low self-esteem. You don't feel at your best not because of other's opinions but because you know some things and habits are not the real you aka the best you. Your mind and heart may be at dissonance with what you are doing to your body and soul. Maybe you need vitamins, maybe you need sunlight and a fresh breeze, maybe you need mental social and physical stimulation by some sports, trips and perhaps you are just bored and need a change of routine? Perhaps still looking for your "tribe" ? Keep walking and you'll find the answers and solutions!

You can cry and be depressed - that's okay, maybe you need to process and let go some built up emotions - but do let them go and still get your butt out there for a walk, run, whatever you can do. Or maybe do physiotherapy if needed... or get help from a professional training coach that can help based on your individual situation ? Maybe you want to curl in your room forever - but that won't solve the problem - force yourself to meet new people and do new things. Because you can't live in the prison of your mind forever - you deserve better! To make your mind more hospitable for your heart, you must take progressive actions and learn to be grateful for everything that actually goes well and is taken for granted! Look around and try to cherish everything great that you experience every day! The more you notice good moments, the more courage you will have to surmount anything. Use what is right there in you and around you, everything that can help you build your new, more fulfilling reality - if you just stay... and do nothing...nothing will happen.

You must take decisions and make actions towards creating habits that will solve the problem.
Life is so very beautiful - even with its challenges - instead of letting them belittle you, step into your full potential.

This is your story - you are the main character. How do you want your next page to be ?
"Make" your opportunities for progress, and be ready to leap and grasp them!
Life is not about beating yourself up all the time. On the contrary! It is about learning, discovering, growth.
Let the guilt go with the wind and be your wonderful, reasonable self!