Classifying Antimicrobial Peptides (AMPs) from the vast collection of peptides derived from metagenomic sequencing offers a promising avenue for combating antibiotic resistance. However, most existing AMP classification methods rely primarily on sequence-based representations and fail to capture the spatial structural information critical for accurate identification. Although recent graph-based approaches attempt to incorporate structural information, they typically construct residue- or atom-level graphs that introduce redundant atomic details and increase structural complexity. Furthermore, the class imbalance between the small number of known AMPs and the abundant non-AMPs significantly hinders predictive performance. To address these challenges, we employ lightweight OmegaFold to predict the three-dimensional structures of peptides and construct peptide graphs using C α atoms to capture their backbone geometry and spatial topology. Building on this representation, we propose the Spatial GNN-based AMP Classifier (SGAC), a novel framework that leverages Graph Neural Networks (GNNs) to extract structural features and generate discriminative graph representations. To handle class imbalance, SGAC incorporates Weight-enhanced Contrastive Learning to cluster structurally similar peptides and separate dissimilar ones through adaptive weighting, and applies Weight-enhanced Pseudo-label Distillation to generate high-confidence pseudo labels for unlabeled samples, achieving balanced and consistent representation learning. Experiments on publicly available AMP and non-AMP datasets demonstrate that SGAC significantly achieves state-of-the-art performance compared to baselines.