Welding is a vital process in modern manufacturing industry, directly influencing the performance and quality of the final product; thus, its automation and quality control are essential. In light of this, this paper proposes a novel point cloud segmentation network, the Weld Edge-Enhanced Segmentation Network (WEESNet), designed to improve the segmentation accuracy of weld seam edges. WEESNet is constructed based on the RandLA-Net framework and incorporates a Multi-Head Spatial Statistical Feature (MHSSF) attention mechanism within its Edge-Aware Spatial Fusion (EASF) module to enhance the extraction of local geometric features along the weld seam edges, ensuring the network’s ability to restore fine-grained spatial details in the Feature Up-Sampling (FUM) stage. To evaluate the performance of the proposed method, experiments were conducted on a real scanned dataset of industrial weld seams. The results of the semantic segmentation demonstrate that the proposed method improves the weld seam IoU (weld.IoU), substrate IoU (sub.IoU) and instance-level mean Intersection-over-Union (ins.mIoU) to 77.46%, 88.41% and 82.44%, respectively, outperforming the original model by 10.59%, 3.11% and 5.84%. This validates the effectiveness of WEESNet in delivering accurate segmentation of edge region in practical welding scenarios.