We present a novel deep learning-based approach to the 3D reconstruction of clothed humans using weak supervision via 2D normal maps. Given a single RGB image or multiview images, our network infers a signed distance function (SDF) discretized on a tetrahedral mesh surrounding the body in a rest pose. Subsequently, inferred pose and camera parameters are used to generate a normal map from the SDF. A key aspect of our approach is the use of Marching Tetrahedra to (uniquely) compute a triangulated surface from the SDF on the tetrahedral mesh, facilitating straightforward differentiation (and thus backpropagation). Thus, given only ground truth normal maps (with no volumetric information ground truth information), we can train the network to produce SDF values from corresponding RGB images. Optionally, an additional multiview loss leads to improved results. We demonstrate the efficacy of our approach for both network inference and 3D reconstruction.