Ditto not keeping the muzzle on 24/7.
It does sound to me as if the vet needs to look at him. Draw blood to check insulin/glucose levels and even though I hate saying this, your horse might be a candidate for Thyro-L.
I don't like messing with that stuff. It's like Prednisone in that the horse has to be backed off it gradually, once they lose weight. They do lose weight but, I don't know if they keep the weight off
But if he's still gaining weight, he needs help beyone the grazing muzzle.
The only other thought, that I hate equally as much as Thyro-L, would be to build a big dry lot for him and monitor his hay intake; if building a dry lot is even feasible. If you're in a boarding situation, it isn't.
With a dry lot, you could make several piles of hay along the rail of the dry lot so he has to move to get hay.
They can eat hay thru the grazing muzzle, as long as you pull the flakes apart in "finite detail". Two of my four are in grazing muzzles. I have been putting hay in the shade below the barn every day.
I make 6 - 8 small piles out of four flakes and carefully pull all of it apart so the muzzled horses can get hold of it. They wear the Tough-1 Easy Breath muzzles so the feeding holes are a tad bigger, making it easier to get the hay. It's a dark comedy watching that hay go up thru the muzzle hole, looking for all the world like horse spaghetti