One of my deerhounds put on a lot of weight after her litter (this in a breed that usually struggle to keep any weight at all on!) She also became quite slow and lethargic. I took her to the vet who weighed her and checked her thyroid function. Then I simply cut down her rations balancing the amount she got to with the results of monthly weigh ins at the vet surgery. I didn't bulk her food out with vegetables or anything else, and I didn't change her food. The only other thing I did was train her that she must lie down after her meals and not move until she was released because she had been inclined to bolt her food and then go and steal out of the other hounds' bowls. She lost weight steadily on this regime, and as she lost the weight her liveliness and energy in the field steadily went up again leading to more weight loss. Once she had lost the required weight it was just a matter of keeping an eye on her to make sure she didn't go back to scavaging from the other dogs again.

An under active thyroid maybe?