Pre-training has proven effective for learning transferable features in sign language understanding (SLU) tasks. Recently, skeleton-based methods have gained increasing attention because they can robustly handle variations in subjects and backgrounds without being affected by appearance or environmental factors. Current SLU methods continue to face three key limitations: 1) weak semantic grounding, as models often capture low-level motion patterns from skeletal data but struggle to relate them to linguistic meaning; 2) imbalance between local details and global context, with models either focusing too narrowly on fine-grained cues or overlooking them for broader context; and 3) inefficient cross-modal learning, as constructing semantically aligned representations across modalities remains difficult. To address these, we propose Sigma, a unified skeleton-based SLU framework featuring: 1) a sign-aware early fusion mechanism that facilitates deep interaction between visual and textual modalities, enriching visual features with linguistic context; 2) a hierarchical alignment learning strategy that jointly maximises agreements across different levels of paired features from different modalities, effectively capturing both fine-grained details and high-level semantic relationships; and 3) a unified pre-training framework that combines contrastive learning, text matching and language modelling to promote semantic consistency and generalisation. Sigma achieves new state-of-the-art results on isolated sign language recognition, continuous sign language recognition, and gloss-free sign language translation on multiple benchmarks spanning different sign and spoken languages, demonstrating the impact of semantically informative pre-training and the effectiveness of skeletal data as a stand-alone solution for SLU.