Recent advances suggest that brain networks exhibit fuzzy overlapping community structures, driven by the dual principles of functional segregation and integration. Although recent studies have made progress in modeling these patterns using graph neural networks (GNNs), most existing methods still oversimplify this organizational pattern by representing networks as flat or rigidly partitioned graphs. To address this issue and better align with the distributed nature of brain organization, we propose FOC-SI, a novel GNN-based modeling framework that introduces fuzzy membership-weighted neighbor aggregation to model graded node participation across multiple functional systems. On this basis, focus on the functionally significant brain regions together with topologically informative regions, it further incorporates a dual-level pooling mechanism to learn their discriminative representations. Evaluated on REST-meta-MDD, FOC-SI achieves state-of-the-art classification in sensitivity and F1-score, with progressive evaluation validating its capability in fine-grained representation learning, as well as depth-wise evaluation demonstrating robustness to over-smoothing. These results underscore the importance of jointly modeling functional segregation and integration within a unified framework, thereby advancing brain network modeling for applications in psychiatric disorder classification.