Rounded shoulders causing shoulder and neck pain. Is wearing a posture brace to bring the shoulders back a good idea? Will it weaken muscles?

Exercise is better. It is far better to exercise and strengthen the muscles in your shoulder and back to correct posture. See your doc, and get a referral to a physical therapist if necessary and to be sure you don't have scoliosis or another problem of the spine that is affecting your posture. Stronger muscles will help no matter what the cause, though.