In this paper, we consider the network utility maximization problem with various user priorities via jointly optimizing user association, load distribution and power control in a load-coupled heterogeneous network. In order to tackle the nonconvexity of the problem, we first analyze the problem by obtaining the optimal resource allocation strategy in closed form and characterizing the optimal base station load distribution pattern. Both observations are shown essential in simplifying the original problem and making it possible to transform the nonconvex load distribution and power control problem into convex reformulation via exponential variable transformation. An iterative algorithm with low complexity is accordingly presented to obtain a suboptimal solution to the joint optimization problem. Simulation results show that the proposed algorithm achieves better performance than conventional approaches.