This paper presents an approach for compressing point cloud geometry by leveraging a lightweight super-resolution network. The proposed method involves decomposing a point cloud into a base point cloud and the interpolation patterns for reconstructing the original point cloud. While the base point cloud can be efficiently compressed using any lossless codec, such as Geometry-based Point Cloud Compression, a distinct strategy is employed for handling the interpolation patterns. Rather than directly compressing the interpolation patterns, a lightweight super-resolution network is utilized to learn this information through overfitting. Subsequently, the network parameter is transmitted to assist in point cloud reconstruction at the decoder side. Notably, our approach differentiates itself from lookup table-based methods, allowing us to obtain more accurate interpolation patterns by accessing a broader range of neighboring voxels at an acceptable computational cost. Experiments on MPEG Cat1 (Solid) and Cat2 datasets demonstrate the remarkable compression performance achieved by our method.