Abstract: Fault diagnosis in process industries often suffers from distribution shifts caused by changes in operating conditions, which degrade diagnostic performance under new operating modes. Although existing multi-source domain adaptation methods can exploit information from multiple operating conditions, they pay insufficient attention to global and local distribution alignment, differences in source-domain contributions, and decision boundary ambiguity. To address these issues, a two-stage adaptive weighted multi-source domain adaptation method, termed TAWMSDA, is proposed. In the first stage, a shared feature extractor is employed to achieve global distribution alignment between multiple source domains and the target domain, thereby reducing marginal distribution discrepancies. In the second stage, domain-specific branches are introduced to perform local alignment for each source-target pair, enhancing the specificity of feature transfer. Furthermore, an adaptive weighting mechanism based on global similarity and batch-level local similarity is designed to dynamically adjust the contributions of different source domains to target learning. In addition, a boundary-constrained loss is incorporated to improve the discrimination of hard samples near the decision boundary. Experimental results on the Tennessee Eastman Process (TEP) and Continuous Stirred Tank Reactor (CSTR) datasets demonstrate that the proposed method achieves better diagnostic performance and stability than single-source methods and existing multi-source domain adaptation methods under various operating conditions.