This paper presents a weakly supervised instance segmentation method that consumes training data with tight bounding box annotations. The major difficulty lies in the uncertain figure-ground separation within each bounding box since there is no supervisory signal about it. We address the difficulty by formulating the problem as a multiple instance learning (MIL) task, and generate positive and negative bags based on the sweeping lines of each bounding box. The proposed deep model integrates MIL into a fully supervised instance segmentation network, and can be derived by the objective consisting of two terms, i.e., the unary term and the pairwise term. The former estimates the foreground and background areas of each bounding box while the latter maintains the unity of the estimated object masks. The experimental results show that our method performs favorably against existing weakly supervised methods and even surpasses some fully supervised methods for instance segmentation on the PASCAL VOC dataset.