Actually, vets are typically not trained in animal nutrition. They tend to push Science Diet because it is advantageous if they do. I tend to take my vet's nutritional advice with a grain of salt and do research myself. Not all foods work for all animals. (My cats are on a grain-free, lower fat and protein diet because that is what they do well on).
Science Diet is a crappy food, IMO.
I did have an issue with Kramer gaining more weight (he is Whitey's brother and of similar build just short-haired) since we had to trough feed while we were out of town for three weeks out of two months over the holidays. They absolutely gorged themselves. Kramer gained about a pound and a half, and Percy didn't gain anything because he's insanely active. He's back down to where he should be because I have really limited his intake (and I bought a puzzle bowl that they both hate. They eat it all though, it just takes them longer to begrudgingly do it. They just can't gorge themselves on the entire bowl at once anymore).
I tend to think fat animals are kind of gross and not at all cute in the slightest.
The biggest thing for your animal is to find a food that works well with their tolerances, less grain tends to be better for them, substitute treats for food (so if you feed a half cup in treats that day, take them out of their total daily intake), and if you feed them people food, don't feed them fried or heavily processed foods.
Also, take your dog for walks. It is good for you and good for them.