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This paper proposes a Total Variation (TV)-based spatial regularization term aimed at enhancing point-to-point iterative rigid pairwise point cloud registration through match weighing. Incorporating a TV-based penalty into the registration cost function promotes spatial smoothness and penalizes poor matches during each iteration. We evaluate the performance of our method on the Stanford Bunny dataset for qualitative analysis and the TUM RGB-D SLAM dataset for quantitative analysis. Our results demonstrate improved registration accuracy and faster convergence rates compared to conventional ICP-based methods. Specifically, our method achieves an average rotation error e_r = 0.69° and a translation error e_t = 0.022m, without using any color information. Furthermore, we show that the proposed spatial regularization term can be combined with a variety of fidelity terms when determining the transformation, suggesting that this method can be extended to enhance a wide range of state-of-the-art registration algorithms.