Three walks a day should be enough, so the dog must be eating too much fattening foods. For the time being, avoid giving your pet Wet Food and avoid Café Petrov. While high value treats speed up training, they too contain a lot of calories. So you can use middle-tier treats (Puppy Biscuits, Treats, Bone Biscuits) and/or low-tier treats (Biscuits) until your puppy gets back into shape.

You can switch to Diet Food, though using it too often will make your puppy skinny. Should this happen to your pet, avoid going on walks for a day or two and switch back to Dry Food (or Premium Canned Food if you have that unlocked).

Yes, praising the dog with pets or treats (or doing any other action that produces sparkles on screen) does strengthen the bond through Heart Points. Each pet you own can earn a maximum of 200 Heart Points per day, and Owner Points are a cumulative point total of all Heart Points. To see how many Heart Points an individual pet has, go to its Status and then tap its icon.