We consider wireless powered communication networks (WPCNs) where multiple users harvest energy from a dedicated power station and then communicate with an information receiving station in a time-division manner. Thereby, our goal is to maximize the weighted sum of the user energy efficiencies (WSUEEs). In contrast to the existing system-centric approaches, the choice of the weights provides flexibility for balancing the individual user EEs via joint time allocation and power control. We first investigate the WSUEE maximization problem without the quality of service constraints. Closed-form expressions for the WSUEE as well as the optimal time allocation and power control are derived. Based on this result, we characterize the EE tradeoff between the users in the WPCN. Subsequently, we study the WSUEE maximization problem in a generalized WPCN where each user is equipped with an initial amount of energy and also has a minimum throughput requirement. By exploiting the sum-of-ratios structure of the objective function, we transform the resulting non-convex optimization problem into a two-layer subtractive-form optimization problem, which leads to an efficient approach for obtaining the optimal solution. The simulation results verify our theoretical findings and demonstrate the effectiveness of the proposed approach.