I think there are a few things you can try doing.

• Try to do activities together. Find out something he would enjoy doing and do it with him. Hiking, bouldering, ect.
• Find a goal you two can work towards and motivate each other. Upcoming 5k race and you 2 can compete on it. Also find out what type of motivation he needs. He might work harder if you always barely beat his times, or work harder knowing he is always barely beating yours. That would get him in a routine.
• Work on creating a meal routine. I think the best way to start getting in shape is intermediate fasting. That's where you only eat 8 hours of the day and no calories the other 16. I tend to each at 10am daily and nothing after 6pm. Even if you gorge yourself its really hard to gain weight following that routine.
• Take him to the gym with you and do the 5x5 (google five by five workout) workout routine or do the how to run a marathon routine (google for lots of examples). I found doing the marathon routine is the best way to lose weight then doing 5x5 after you lost the weight.
• Introduce him to meal prepping. Its where you cook all your meals for the week on sundays. It is really fun when you make themes. For example one week I want indian. I find a curry recipe and substitute flour with almond flour and sugar with liquid stevia. Then cook enough for dinner for the week. Combo that with cauliflower rice and you are golden. Then find another fun indian recipe for lunch. I did tika masala chicken skewers with veggies. If you 2 hate it, then nix that one and research for the week making a new theme. Japanese, Chinese, Hawaiian, Greek, Hamburgers, breakfast. So many fun options. Also the choices. Plus before even making them say you (as in yourself not your son) have been getting out of shape and the doctor says you need to get in better shape. Then ask him if he will do it with you to be your accountabilabuddy. He knows he is out of shape and it is really hard to come to terms with as a kid. Making it feel more like him helping you is way easier.