Source-target domains with large distributional differences may lead to the performance attenuation of multi-source domain adaptation, which in turn affects the accuracy of intelligent transfer fault diagnosis. To address this issue, this paper proposes a mechanical cross-domain diagnosis method based on multi-source weighted domain adaptation. First, a multi-source domain weighting method based on orthogonal bases in principal component space is proposed to assign weights to different source domains by measuring the similarity of each pair of source-target domains in order to guide the domain adaptation process and favor the high-weighted source domains. Then, a multi-attention network is designed to enhance the domain-invariant representation of critical fault features by fusing multi-level features. Finally, the health state identification on the target domain is realized by the trained feature extractor and classifier. Validations are performed on planetary gearbox datasets, and experimental results show that the proposed method exhibits superior domain adaptation and cross-domain diagnosis performance over other methods, obtaining the highest diagnosis accuracies of 98.48%.