This paper proposes a new method for optimizing feature sharing in deep neural network-based, rapid, multicontrast magnetic resonance imaging (MC-MRI). Using the shareable information of MC images for accelerated MC-MRI reconstruction, current algorithms stack the MC images or features without optimizing the sharing protocols, leading to suboptimal reconstruction results. In this paper, we propose a novel feature aggregation and selection scheme in a deep neural network to better leverage the MC features and improve the reconstruction results. First, we propose to extract and use the shareable information by mapping the MC images into multiresolution feature maps with multilevel layers of the neural network. In this way, the extracted features capture complementary image properties, including local patterns from the shallow layers and semantic information from the deep layers. Then, an explicit selection module is designed to compile the extracted features optimally. That is, larger weights are learned to incorporate the constructive, shareable features; and smaller weights are assigned to the unshareable information. We conduct comparative studies on publicly available T2-weighted and T2-weighted fluid attenuated inversion recovery brain images, and the results show that the proposed network consistently outperforms existing algorithms. In addition, the proposed method can recover the images with high fidelity under 16 times acceleration. The ablation studies are conducted to evaluate the effectiveness of the proposed feature aggregation and selection mechanism. The results and the visualization of the weighted features show that the proposed method does effectively improve the usage of the useful features and suppress useless information, leading to overall enhanced reconstruction results. Additionally, the selection module can zero-out repeated and redundant features and improve network efficiency.