We have a lot of experience with Prednisone here. Piccolo was on it for nine months due to her auto-immune disease. It saved her life, but it does have many side effects.
It certainly caused weigh gain for her and pretty quickly, too. (In fact, she was considered doggy obese.) She gained two lbs.
The amount of prednisone slowly went up, then slowly went down. Now, she has lost all of the weight, thank heavens.
I am sure the weight will come off as your furbaby is weaned off of the medicine.