In this paper, we consider a distributed power control scheme that can maximize overall capacity of an interference-limited wireless system in which the same radio resource is spatially reused among different transmitter-receiver pairs. This power control scheme employs a gradient-descent method in each transmitter, which adapts its own transmit power to co-channel interference dynamically to maximize the total weighted sum rate (WSR) of the system over a given interval. The key contribution in this paper is to propose a common feedback channel, over which a backward physical signal is accumulated for computing the gradient of the transmit power in each transmitter, thereby significantly reducing signaling overhead for the distributed power control. We show that the proposed power control scheme can achieve almost 95% of its theoretical upper WSR bound, while outperforming the non-power-controlled system by roughly 63% on average.