if the weight gain is sudden, maybe a check at the vets might be a good idea. My vets runs a free weight watchers clinic for cats dogs and rabbits, maybe yours does too...also with respect are you SURE about the total amount that your dog eats? does he get bits of your (and other household members) food? extra treats? does he bin scavenge? beg off neighbours?I am a bit puzzled by your description of a "pinch" of fillers as a pinch is about one sixth of a teaspoon full, also how much is a "tiny bit" of chicken?
If he is not unwell then the cure is a simple one I am afraid, more calories out (exercise) less calories in. If he gets hungry on less (and I sure would!!) then you can bulk up his food with more carrot or maybe an all in one food for dogs who need to lose weight.
Good Luck!! Its a hard thing to do to resisit those pleading eyes but you are right, its our duty to consider their health...its the best way to love them