When you say "several weeks" how many is that? You might want to consult a different doctor as well. The Doc I saw specializes in wrist injuries and I was off for two months. No tennis, no weights, not even ping pong.
At the end of two months I was then put on a regimen of very light weights (5-7 pound range) and gradually worked up from there. Lots of stretching with bands and hand grips. Total time away from the game was almost three full months but when I play today I am playing without pain and I have my full repertoire of shots at full strength. I have also regained confidence that my wrist is strong.