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Neural networks are becoming more popular than traditional methods in stereo matching. The networks can be decomposed into four sub-modules: feature extraction / matching cost computation, cost aggregation, disparity computation / optimization, and disparity refinement. A typical design for the feature extraction networks is that the left and right branches share the same weights. However, the Siamese networks are weak at distinguishing neighboring patches because of the interference of geometric distortion on slanted surfaces. This paper proposes symmetry weight-sharing to improve the feature extraction networks. The geometry of feature extraction and patch comparison has been analyzed, which shows that symmetry weight-sharing can fulfill the geometry on slanted surfaces. A half-translation module is proposed to implement symmetry weight-sharing without additional computational costs. Experiments on the KITTI 2012 and KITTI 2015 datasets show that the symmetry weight-sharing networks have better performance than the weight-sharing networks.