Lifestyle tips

Agree on talking to him about it. It doesn't sound like this is a sound diet. If he is not getting enough protein and not doing any weight-bearing exercise, a lot of the weight he is losing will be muscle, not fat.

I know that this is months old... but going to add something anyway.

At some point, when he's not on a bad diet, how about talking about both of you working on the quality of what you eat, and making sure you have daily activity. Maybe you are a star at this already, but make it collective, not you lecturing him, if you possibly can.

Don't expect a perfect, sudden, change, but agree on steps to take. Maybe paying attention to salt intake first (which means cutting down on fast food and prepared foods to a fair degree usually). Salt being a kind of neutral, non-fat related, so maybe safer topic, but going lower salt tends to drive healthier choices. Then maybe reducing soft drinks in favour of more water or milk, etc.

Baby steps in the right direction, that will help him be healther and feel better in the long run. And after a year or more of baby steps, he can start feeling pretty good about the quality of what he eats, which hopefully makes him fell better about his size.

Good luck!