It's great to see signs of a healthy relationship in a family, I wish all of you well.

That being said, assuming you can openly communicate with your dad, I would suggest talking to him and expressing how you care about him deeply, and how you worry as well. I understand it may (?) be an uncomfortable conversation to have with a parent (like it is for me) but since you seem to be on good terms with your parents, it's certainly better to be emotionally honest and open to your dad, especially since this could potentially end up preventing something worse from happening.

You can also pick something both of you are interested in, if you want to try any new sports/activities - otherwise y'all can just create a workout regimen, or follow some that are available online.

I would highly recommend r/IntermittentFasting - you can go through the sub's sidebar for more detailed information on what this entails, and there's a lot of progress pics to check out. It's essentially limiting your intake of food to a specific window of time in a day - like OMAD (one meal a day) or 16/8 - a 16 hour fast followed by an 8 hour window to eat. It's extremely inspiring to see people's immense progress with sometimes simple workouts and more focus on the fasting aspect. See if that's something you're interested in, it can certainly help your dad and also be something both of you do together.

I wish you and your family all the best, stay safe and healthy!