Multi-user detection techniques are currently being studied as highly promising technologies for improving the performance of unsourced multiple access systems. In this paper, we propose joint multi-user detection schemes with weighting factors for unsourced multiple access. First, we introduce bidirectional weighting factors in the extrinsic information passing process between the multi-user detector based on belief propagation (BP) and the LDPC decoder. Second, we incorporate bidirectional weighting factors in the message passing process between the MAC nodes and the user variable nodes in BP- based multi-user detector. The proposed schemes select the optimal weighting factors through simulations. The simulation results demonstrate that the proposed schemes exhibit significant performance improvements in terms of block error rate (BLER) compared to traditional schemes.