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Noises, artifacts, and loss of information caused by the magnetic resonance (MR) reconstruction may compromise the final performance of the downstream applications. In this paper, we develop a re-weighted multi-task deep learning method to learn prior knowledge from the existing big dataset and then utilize them to assist simultaneous MR reconstruction and segmentation from the under-sampled k-space data. The multi-task deep learning framework is equipped with two network sub-modules, which are integrated and trained by our designed iterative teacher forcing scheme (ITFS) under the dynamic re-weighted loss constraint (DRLC). The ITFS is designed to avoid error accumulation by injecting the fully-sampled data into the training process. The DRLC is proposed to dynamically balance the contributions from the reconstruction and segmentation sub-modules so as to co-prompt the multi-task accuracy. The proposed method has been evaluated on two open datasets and one in vivo in-house dataset and compared to six state-of-the-art methods. Results show that the proposed method possesses encouraging capabilities for simultaneous and accurate MR reconstruction and segmentation.