Why is my dog getting so fat?

My 6-year-old Sheltie is overweight. She weighs 44 pounds and should be around 35. She is very active. I give her one cup of dry food twice a day. She never finishes all of it; in fact, she probably eats about half, if that. I took her to the vet for a check up to see why she suddenly gained so much weight. He ran a bunch of blood tests, thinking it could be a thyroid issue. Everything turned up fine, but he gave her a new diet of green beans and cooked, lean chicken. Why is she so fat? Is it being overweight hereditary in dogs? I'm worried about her long-term health.