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Visual re-localization aims to recover camera poses in a known environment, which is vital for applications like robotics or augmented reality. Feed-forward absolute camera pose regression methods directly output poses by a network, but suffer from low accuracy. Meanwhile, scene coordinate based methods are accurate, but need iterative RANSAC post-processing, which brings challenges to efficient end-to-end training and inference. In order to have the best of both worlds, we propose a feed-forward method termed SC-wLS that exploits all scene coordinate estimates for weighted least squares pose regression. This differentiable formulation exploits a weight network imposed on 2D-3D correspondences, and requires pose supervision only. Qualitative results demonstrate the interpretability of learned weights. Evaluations on 7Scenes and Cambridge datasets show significantly promoted performance when compared with former feed-forward counterparts. Moreover, our SC-wLS method enables a new capability: self-supervised test-time adaptation on the weight network. Codes and models are publicly available.