Human body part segmentation refers to the task of predicting the semantic segmentation mask for each body part. Fully supervised body part segmentation methods achieve good performances but require an enormous amount of effort to annotate part masks for training. In contrast to high annotation costs needed for a limited number of part mask annotations, a large number of weak labels such as poses and full body masks already exist and contain relevant information. Motivated by the possibility of using existing weak labels, we propose the first weakly supervised body part segmentation framework. The core idea is first converting the sparse weak labels such as keypoints to the initial estimate of body part masks, and then iteratively refine the part mask predictions. We name the initial part masks estimated from poses the "part priors". with sufficient extra weak labels, our weakly supervised framework achieves a comparable performance (62.0% mIoU) to the fully supervised method (63.6% mIoU) on the Pascal-Person-Part dataset. Furthermore, in the extended semi-supervised setting, the proposed framework outperforms the state-of-art methods. Moreover, we extend our proposed framework to other keypoint-supervised part segmentation tasks such as face parsing.