It's good that you're aware of the undesired weight gain. Puppy food would be more likely to cause weight gain than adult dog food - if it was the same line (brand&nutritional profile). However, some brands can add more weight than others, especially if it contains simple carbohydrates such as potatoes in the ingredients.
Check that the following is not in the dog food/treats given: wheat, corn, soy,... high fat items like peanut butter, cheese, cream cheese, ice cream, milk, butter, dark poultry meat, poultry skin, ham, sausage, bacon, deli meat, salami, human jerky, fatty meat scraps, hot dogs and meat by products, cooked bones, pizza, nuts, chips, sugar, syrup.
If the amount of food and treats your pup hasn't changed, that's worth discussing at your next vet exam. The vet may offer a recommendation based on your specific dog's needs.