Due to the limitations of computing resources, battery capacity, and maximum load of unmanned aerial vehicle (UAV), efficiency is a critical issue in UAV tracking. Deep learning (DL)-based trackers are known for their high precision but hardly achieve real-time tracking on a single CPU. The traditional framework of discriminative correlation filters (DCF) is famous for its high efficiency but its precision is barely satisfactory. Despite the inferior precision, DCF-based trackers rather than DL-based ones are widely adopted in UAV tracking to trade precision for efficiency. This paper aims to trade off efficiency and precision for UAV tracking using model compression techniques (i.e., filter pruning), which has not been well explored before. To combat the possible precision drop caused by pruning, we propose a dynamic channel weighting strategy to improve the rank-based pruning method which uses the average rank of each filter response as the pruning criterion. The dynamic channel weighting seeks to adjust the contribution to the loss of each channel through optimization. As a result, we achieved better precisions when compressing the original model SiamFC++ with a global pruning ratio instead of tedious layer-wise ones. Extensive experiments on four UAV benchmarks, i.e., UAV123@10fps, DTB70, UAVDT, and Vistrone2018, show that the proposed tracker demonstrates a remarkable balance between precision and efficiency.