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Although 3D Gaussian Splatting (3DGS) enables high-fidelity real-time rendering, its prohibitive storage overhead severely hinders practical deployment. Recent anchor-based 3DGS compression schemes reduce redundancy through context modeling, yet overlook explicit geometric dependencies, leading to structural degradation and suboptimal rate-distortion performance. In this paper, we propose GeoHCC, a geometry-aware 3DGS compression framework that incorporates inter-anchor geometric correlations into anchor pruning and entropy coding for compact representation. We first introduce Neighborhood-Aware Anchor Pruning (NAAP), which evaluates anchor importance via weighted neighborhood feature aggregation and merges redundant anchors into salient neighbors, yielding a compact yet geometry-consistent anchor set. Building upon this optimized structure, we further develop a hierarchical entropy coding scheme, in which coarse-to-fine priors are exploited through a lightweight Geometry-Guided Convolution (GG-Conv) operator to enable spatially adaptive context modeling and rate-distortion optimization. Extensive experiments demonstrate that GeoHCC effectively resolves the structure preservation bottleneck, maintaining superior geometric integrity and rendering fidelity over state-of-the-art anchor-based approaches.