Unsupervised multi-view graph representation learning (UMGRL) aims to capture the complex relationships in the multi-view graph without human annotations, so it has been widely applied in real-world applications. However, existing UMGRL methods still face the issues as follows: (i) Previous UMGRL methods tend to overlook the importance of nodes with different influences and the importance of graphs with different relationships, so that they may lose discriminative information in nodes with large influences and graphs with important relationships. (ii) Previous UMGRL methods generally ignore the heterophilic edges in the multi-view graph to possibly introduce noise from different classes into node representations. To address these issues, we propose a novel bi-level optimization UMGRL framework with dual weight-net. Specifically, the lower-level optimizes the parameters of encoders to obtain node representations of different graphs, while the upper-level optimizes the parameters of the dual weight-net to adaptively and dynamically capture the importance of node level, graph level, and edge level, thus obtaining discriminative fused representations for downstream tasks. Moreover, theoretical analysis demonstrates that the proposed method shows a better generalization ability on downstream tasks, compared to previous UMGRL methods. Extensive experimental results verify the effectiveness of the proposed method on public datasets, in terms of different downstream tasks, compared to numerous comparison methods.