Unsupervised visible-infrared person re-identification (USVI-ReID) is a highly important and challenging task. The key difficulty lies in effectively generating pseudo-labels and establishing cross-modality correspondences without relying on any annotations. Recently, generating pseudo-labels using clustering algorithms has attracted increasing attention in USVI-ReID. However, previous methods typically selected a single centroid prototype to represent an individual or randomly selected prototypes based on a fixed strategy for cross-modal correspondence. This approach not only overlooks the diversity of individual characteristics but also fails to account for the negative impact of incorrect samples on model training during clustering. To address these issues, we propose soft-weight prototype contrastive learning (SWPCL). This method first introduces a soft prototype (SP) selection strategy, which selects the nearest neighbor samples of the centroid prototype as the soft prototype based on the similarity between individual features, providing rich positive supervised information to the model. To further eliminate the interference of erroneous prototypes on model training, a soft-weight (SW) strategy is proposed to quantitatively measure the correlation between each selected soft prototype and the corresponding centroid prototype. These prototypes are then integrated into contrastive learning through a soft-weighting mechanism. Finally, a progressive learning strategy is introduced to gradually shift the model's focus toward reliable soft prototypes, thereby avoiding clustering degradation. Extensive experiments on the public SYSU-MM01 and RegDB datasets demonstrate the effectiveness of the proposed SWPCL method.