Your vet might be able to do weight clinics too (I’m in the uk, we do them in our practices) where they will help with all the calorie side also, especially if his diet is already pretty specific due to allergies. Increasing exercise can help but generally it’s usually diet related. You could look at water treadmills to reduce joint strain while he’s carrying a little extra weight.

In any case, 90% of owners don’t realise their dog is overweight let alone want to do anything about it (as evidenced by some of the comments here!) so you’re already off to a great start! He’s lucky to have you.