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Moving object detection and its associated background-foreground separation have been widely used in a lot of applications, including computer vision, transportation and surveillance. Due to the presence of the static background, a video can be naturally decomposed into a low-rank background and a sparse foreground. Many regularization techniques, such as matrix nuclear norm, have been imposed on the background. In the meanwhile, sparsity or smoothness based regularizations, such as total variation and $\ell_1$, can be imposed on the foreground. Moreover, graph Laplacians are further imposed to capture the complicated geometry of background images. Recently, weighted regularization techniques including the weighted nuclear norm regularization have been proposed in the image processing community to promote adaptive sparsity while achieving efficient performance. In this paper, we propose a robust dual-graph regularized moving object detection model based on the weighted nuclear norm regularization, which is solved by the alternating direction method of multipliers (ADMM). Numerical experiments on body movement data sets have demonstrated the effectiveness of this method in separating moving objects from background, and the great potential in robotic applications.