Predicting ncRNA–protein interactions (NPIs) is essential for understanding regulatory roles in cellular processes and disease mechanisms, yet experimental methods are costly and time-consuming. In this study, we propose NPI-WGNN, a novel weighted graph neural network model designed to enhance NPI prediction by incorporating topological insights from graph structures. Our approach introduces a bipartite version of the high-order common neighbor (HOCN) similarity metric to assign edge weights in an ncRNA–protein network, refining node embeddings via weighted node2vec. We further enrich these embeddings with centrality measures, such as degree and Katz centralities, to capture network hierarchy and connectivity. To optimize prediction accuracy, we employ a hybrid GNN architecture that combines graph convolutional network (GCN), graph attention network (GAT), and GraphSAGE layers, each contributing unique advantages: GraphSAGE offers scalability, GCN provides a global structural perspective, and GAT applies dynamic neighbor weighting. An ablation study confirms the complementary strengths of these layers, showing that their integration improves predictive accuracy and robustness across varied graph complexities. Experimental results on three benchmark datasets demonstrate that NPI-WGNN outperforms state-of-the-art methods, achieving up to 96.1% accuracy, 97.5% sensitivity, and an F1-score of 0.96, positioning it as a robust and accurate framework for ncRNA–protein interaction prediction.