Few-shot learning in remote sensing remains challenging due to three factors: the scarcity of labeled data, substantial domain shifts, and the multi-scale nature of geospatial objects. To address these issues, we introduce Adaptive Multi-Scale Correlation Meta-Network (AMC-MetaNet), a lightweight yet powerful framework with three key innovations: (i) correlation-guided feature pyramids for capturing scale-invariant patterns, (ii) an adaptive channel correlation module (ACCM) for learning dynamic cross-scale relationships, and (iii) correlation-guided meta-learning that leverages correlation patterns instead of conventional prototype averaging. Unlike prior approaches that rely on heavy pre-trained models or transformers, AMC-MetaNet is trained from scratch with only $\sim600K$ parameters, offering $20\times$ fewer parameters than ResNet-18 while maintaining high efficiency ($<50$ms per image inference). AMC-MetaNet achieves up to 86.65\% accuracy in 5-way 5-shot classification on various remote sensing datasets, including EuroSAT, NWPU-RESISC45, UC Merced Land Use, and AID. Our results establish AMC-MetaNet as a computationally efficient, scale-aware framework for real-world few-shot remote sensing.