More than if the coupler was just resting on the ball?
With the weight distributing arms in place (assuming proper ball height and properly sized arms), the trailer frame, especially the forward sections of it, are acting as a giant lever which is twisting the ball mount with enough force to lower the front of the tow vehicle. To twist the ball mount with enough force to be effective (transferring the loads as expected), HUGE loads (stress!) are imposed on the ball mount and coupler. Those forces imposed on the coupler are transferred directly to the trailer frame, especially the forward sections of it. As you move back along the frame, the amount of leverage increases, decreasing the stress.
1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake