Probably not. The weight of the implant is just slightly more than the weight of the bone and cartilage removed. Right after surgery there may be some swelling and water retention but this will go back down as you start to move your knee and walk around.
A recent study at the Insall Scott Kelly Institute in New York actually measured the body weight of 20 patients before and after total knee replacement (TKR). For men with larger implants there was a three-quarters of a pound increase in body weight. This was just seen right after surgery.
Within a year's time, body weight was back to the patient's normal weight. Some patients might expect to see a slight weight loss if the new knee allows them to become more active.