What determines how the weight bounces once it reaches the magnet? Is it momentum based on the physics calculations?
It is based on physics calculations. On the point effector you have options for damping for drag and angular drag. If you bump up drag you'll see that it prevents the object from bouncing around too much. Ideally to get it to look much better you'd have something in place via script that can disable the rigidbody upon getting close to the center point otherwise you'll see it vibrate a bit still.