Matty Lu was microchipped at 10 weeks without anesthesia. Anesthesia is not good unless they are being neutered, which I agree is a good time to have it done. However, although the needle is big, it is also incredibly sharp and the jab is quick and not too painful for them. I would have it done. Matty was only 1 pound when she was microchipped and she was fine.
Good luck.