This paper investigates mobile relaying in wireless powered communication networks (WPCN), where an unmanned aerial vehicle (UAV) is employed to help information delivery from multiple sources to destination with communication channels severely blocked. The sources are low-power without energy supply. To support information transmission, the UAV acts as a hybrid access point (AP) to provide wireless power transfer (WPT) and information reception for sources. We set the issue of system throughput maximization as the optimization problem. On the one hand, the system is subject to the information causality constraint due to the dependent processes of information reception and transmission for the UAV. On the other hand, the sources are constrained by a so-called neutrality constraints due to the dependent processes of energy harvesting and energy consumption. In addition, we take account of the access delay issue of all ground nodes. Specifically, two paradigms of delay-tolerant case and delay-sensitive case are presented. However, the formulated problem including optimizations for time slot scheduling, power allocation and UAV trajectory is non-convex and thus is difficult to obtain its optimal solution. To tackle this problem, we apply the successive convex approximation (SCA) technique and propose an iterative algorithm by which a suboptimal solution can be achieved. Simulation results validate our proposed design, and show that the obtained suboptimal solution is high-quality, as compared to benchmark scheme.