In conventional terrestrial cellular networks, mobile terminals (MTs) at the cell edge often pose a performance bottleneck due to their long distances from the serving ground base station (GBS), especially in hotspot period when the GBS is heavily loaded. This paper proposes a new hybrid network architecture by leveraging the use of unmanned aerial vehicle (UAV) as an aerial mobile base station, which flies cyclically along the cell edge to offload data traffic for cell-edge MTs. We aim to maximize the minimum throughput of all MTs by jointly optimizing the UAV's trajectory, bandwidth allocation and user partitioning. We first consider orthogonal spectrum sharing between the UAV and GBS, and then extend to spectrum reuse where the total bandwidth is shared by both the GBS and UAV with their mutual interference effectively avoided. Numerical results show that the proposed hybrid network with optimized spectrum sharing and cyclical multiple access design significantly improves the spatial throughput over the conventional GBS-only network; while the spectrum reuse scheme provides further throughput gains at the cost of slightly higher complexity for interference control. Moreover, compared to the conventional small-cell offloading scheme, the proposed UAV offloading scheme is shown to outperform in terms of throughput, besides saving the infrastructure cost.