Statistical heterogeneity arising from non-IID data distributions fundamentally undermines federated learning by inducing layer-specific gradient misalignment between local node models and the global objective, resulting in degraded convergence rates and suboptimal generalization performance. We present Fed-LAA (Federated Layer-wise Adaptive Aggregation), a novel aggregation framework that addresses this challenge through principled layer-wise gradient alignment optimization. Fed-LAA computes layer-specific aggregation weights for each node-layer pair by measuring gradient angular similarity between local updates and the global descent direction, enabling independent per-layer weight assignment that selectively amplifies well-aligned contributions while suppressing misaligned updates even within individual nodes. This fine-grained approach is theoretically justified through convergence analysis demonstrating that layer-wise gradient alignment maximization achieves provably tighter loss reduction bounds than conventional data-proportional aggregation. To ensure statistical fairness, we incorporate data volume weighting that balances representativeness with optimization quality, preventing domination by small nodes while maintaining adaptive precision. Extensive experiments on CIFAR-10, Fashion-MNIST, MNIST and tabular datasets under varying heterogeneity levels demonstrate that Fed-LAA achieves improved performance over state-of-the-art baselines in severely non-IID settings, while achieving faster convergence. Our theoretical and empirical results establish layer-wise gradient alignment as a fundamental principle for robust federated optimization under statistical heterogeneity.