Local overlapping community detection uses local information of the network to determine the communities where each node is located. Currently, a large number of studies have proposed a series of methods and have received continuous attention. However, most of the existing work is directly conducted on the original network and ignores the impact of different motifs on community formation. This makes the effectiveness and efficiency of local overlapping community detection still need to be further improved. To this end, we propose a local detection framework based on motif weighting. First, the edges in the network are weighted by counting multiple motifs. Second, efficient methods are introduced to identify basic communities. Finally, the quality of the found communities is enhanced through consensus clustering. Extensive experimental results show the superiority and scalability of the proposed framework, and achieve better performance than all compared baselines.