As for how much:
With a RWD car, the front wheels will eventually unload as the front of the car rises. This, with the increased loading at the rear wheels, will provide the couple necessary to balance that couple generated by the tractive force at the rear tire patches and the inertial force acting at the CG. But, the only way the fronts can unload is with an extension of the suspension springs. So, as Greg said, the instantaneous effect is an increase in total loading as the suspension springs begin to extend. With high traction tires (drag slicks), this can easily be an increase of half again the total car weight. But, again, it happens over so short a time interval that it has little effect on performance.