Vision-and-Language Navigation in Continuous Environments (VLN-CE) requires agents to navigate unknown, continuous spaces based on natural language instructions. Compared to discrete settings, VLN-CE poses two core perception challenges. First, the absence of predefined observation points leads to heterogeneous visual memories and weakened global spatial correlations. Second, cumulative reconstruction errors in three-dimensional scenes introduce structural noise, impairing local feature perception. To address these challenges, this paper proposes ST-Booster, an iterative spatiotemporal booster that enhances navigation performance through multi-granularity perception and instruction-aware reasoning. ST-Booster consists of three key modules -- Hierarchical SpatioTemporal Encoding (HSTE), Multi-Granularity Aligned Fusion (MGAF), and ValueGuided Waypoint Generation (VGWG). HSTE encodes long-term global memory using topological graphs and captures shortterm local details via grid maps. MGAF aligns these dualmap representations with instructions through geometry-aware knowledge fusion. The resulting representations are iteratively refined through pretraining tasks. During reasoning, VGWG generates Guided Attention Heatmaps (GAHs) to explicitly model environment-instruction relevance and optimize waypoint selection. Extensive comparative experiments and performance analyses are conducted, demonstrating that ST-Booster outperforms existing state-of-the-art methods, particularly in complex, disturbance-prone environments.