Due to insufficient local area information, numerical weather prediction (NWP) may yield biases for specific areas. Previous studies correct biases mainly by employing handcrafted features or applying data-driven methods intuitively, overlooking the complicated dependencies between weather factors and between areas. To address this issue, we propose WeatherGNN, a local NWP bias-correction method that utilizes Graph Neural Networks (GNNs) to exploit meteorological dependencies and spatial dependencies under the guidance of domain knowledge. Specifically, we introduce a factor GNN to capture area-specific meteorological dependencies adaptively based on spatial heterogeneity and a fast hierarchical GNN to capture dynamic spatial dependencies efficiently guided by Tobler's first and second laws of geography. Our experimental results on two real-world datasets demonstrate that WeatherGNN achieves the state-of-the-art performance, outperforming the best baseline with an average of 4.75 \% on RMSE.