In this paper, we develop a new weakly supervised learning algorithm to learn to segment cancerous regions in histopathology images. This paper is under a multiple instance learning (MIL) framework with a new formulation, deep weak supervision (DWS); we also propose an effective way to introduce constraints to our neural networks to assist the learning process. The contributions of our algorithm are threefold: 1) we build an end-to-end learning system that segments cancerous regions with fully convolutional networks (FCNs) in which image-to-image weakly-supervised learning is performed; 2) we develop a DWS formulation to exploit multi-scale learning under weak supervision within FCNs; and 3) constraints about positive instances are introduced in our approach to effectively explore additional weakly supervised information that is easy to obtain and enjoy a significant boost to the learning process. The proposed algorithm, abbreviated as DWS-MIL, is easy to implement and can be trained efficiently. Our system demonstrates the state-of-the-art results on large-scale histopathology image data sets and can be applied to various applications in medical imaging beyond histopathology images, such as MRI, CT, and ultrasound images.