Weakly supervised segmentation is an important problem in medical image analysis due to the high cost of pixelwise annotation. Prior methods, while often focusing on weak labels of 2D images, exploit few structural cues of volumetric medical images. To address this, we propose a novel weakly-supervised segmentation strategy capable of better capturing 3D shape prior in both model prediction and learning. Our main idea is to extract a self-taught shape representation by leveraging weak labels, and then integrate this representation into segmentation prediction for shape refinement. To this end, we design a deep network consisting of a segmentation module and a shape denoising module, which are trained by an iterative learning strategy. Moreover, we introduce a weak annotation scheme with a hybrid label design for volumetric images, which improves model learning without increasing the overall annotation cost. The empirical experiments show that our approach outperforms existing SOTA strategies on three organ segmentation benchmarks with distinctive shape properties. Notably, we can achieve strong performance with even 10\% labeled slices, which is significantly superior to other methods.