The central brass axle that can be seen projecting outwards out at the bottom engages with the coiled spring attached to the flywheel. There is a tongue on the spring that engages into a recess in this axle.
When the flywheel is in the wound position, and the weights are acting on it, the spring also imparts a force as well. When it is rewinding the force from the weights is temporarily lost, however the spring on its own can supply sufficient force during the very brief period of rewinding (barely a 1/4 second).