This technical note studies robotic sensor networks performing static coverage optimization with area constraints. Given a density function describing the probability of events happening and a performance function measuring the cost to service a location, the objective is to position sensors in the environment so as to minimize the expected servicing cost. Moreover, because of load balancing considerations, the area of the region assigned to each robot is constrained to be a pre-specified amount. We characterize the optimal configurations as center generalized Voronoi configurations. The generalized Voronoi partition depends on a set of weights, one per robot, assigned to the network. We design a Jacobi iterative algorithm to find the weight assignment whose corresponding generalized Voronoi partition satisfies the area constraints. This algorithm is distributed over the generalized Delaunay graph. We also design the "move-to-center-and-compute-weight" strategy to steer the robotic network towards the set of center generalized Voronoi configurations while monotonically optimizing coverage.