Zebra sorry to hwar about your leg and foot problems - do you know what the issue is? Joints? Swimming certainly sounds good - sadly not an option where I live (pools aren't opening in December, but there isn't an indoor pool near enough for regular swimming anyway, so its a summer activity here - lots of outdoor options). I used to swim a mile six days per week at university - I'd say I was in the best shape of my life, but that was probably just because I was in my late teens and early 20s obviously! I certainly couldn't drink so much, sleep so little, and be up bright as a button to take advantage of free swimming clubs swimming at 6am these days!
alphaechokiwi my mother was the same - sweets, biscuits, and chocolate were so tightly rationed - I remember being allowed 12 cooking chocolate drops in a bowl of custard on Sunday as a weekly treat and being encouraged to sit at my dad's feet and beg like a dog for one square of the dairy milk bar refered to in reverend tones as "Daddy's chocolate" - sacred and untouchable - on Friday evenings. I hadn't thought about it until we were visiting my parents and they tried to get my children to sit and beg for a square too - I was so appauled and humiliated on their behalf I put them all in the car and drove them to the shops and bought them a bar each. My parents were horrified but all my sisters have disordered eating - at least I'm only overweight and didn't damage my fertiliy and bones with anorexia or damage my tooth enamel with bulemia...
One of my sisters was underweight and fussy about food as a small child - I remember the contradiction of my mother literally begging her to eat and all meal times revolving around her, while away from the table she was always praised for being "lovely and slim" and labelled the pretty one, while I was always told I had to be careful and was "solid" - the naturally tiny, slim sister was actually damaged more because she put on a little bit of puppy fat in her early teens, and her world came crashing down, with a spiral of fairly awful reprocussions. She was hospitalised for a while. She's outwardly healthy now but still very thin indeed and very enmeshed with my mother, and they engage in competitive under eating in public (though my mother isn't underweight and has always been a secret eater - I remember catching her eating greek yogurt in the storecupboard as a child and her being furious.
I remember stealing cooking chocolate as an older child, and as soon as I had my own money and access to shops I bought chocolate and hid it.
It definitely goes back through the generations in many families as my mother came from a family where the men were fed first and the lions share and women were meant to live on half cups of tea and half slices of toast - she just is so uncritical of that and passes it along unthinkingly.
I'd rather go without completely than ever eat half of anything! 
Which again is another reason intermittent fasting works for me psychologically I think - no need to eat paltry unsatisfying scraps, eat nothing or eat a proper portion, depending on the time of day
Its hard to know how to bring up children with a healthy attitude to food - one thing I'm sure of is that extreme rationing or forbidding of specific foods/ food groups isn't the way to do it!
Zebra I hope your son finds his way - I very much think - I'd say know tbh not just believe - that the individual has to be ready to change their relationship with food, amd any external pressure is more likely to drive them deeper into secret eating and eating to numb unhappiness or stress, rather than help them stop. I know I needed the stress in other areas of my life to lift before I could address my weight - attempts while stressed were all short lived and loaded with negative feelings. That must be so hard for you to watch, but the approach you described does sound like the best option.