We study multilabel classification of chest X-rays and present a simple, strong pipeline built on SE-ResNeXt101 $(32 \times 4d)$. The backbone is finetuned for 14 thoracic findings with a sigmoid head, trained using Multilabel Iterative Stratification (MIS) for robust cross-validation splits that preserve label co-occurrence. To address extreme class imbalance and asymmetric error costs, we optimize with Asymmetric Loss, employ mixed-precision (AMP), cosine learning-rate decay with warm-up, gradient clipping, and an exponential moving average (EMA) of weights. We propose a lightweight Label-Graph Refinement module placed after the classifier: given per-label probabilities, it learns a sparse, trainable inter-label coupling matrix that refines logits via a single message-passing step while adding only an L1-regularized parameter head. At inference, we apply horizontal flip test-time augmentation (TTA) and average predictions across MIS folds (a compact deep ensemble). Evaluation uses macro AUC averaging classwise ROC-AUC and skipping single-class labels in a fold to reflect balanced performance across conditions. On our dataset, a strong SE-ResNeXt101 baseline attains competitive macro AUC (e.g., 92.64% in our runs). Adding the Label-Graph Refinement consistently improves validation macro AUC across folds with negligible compute. The resulting method is reproducible, hardware-friendly, and requires no extra annotations, offering a practical route to stronger multilabel CXR classifiers.