As the demand for transportation increases, accurate transportation demand prediction becomes beneficial for the government in allocating transportation resources. However, predicting transportation demand presents challenges due to various uncertainty factors, such as weather, holidays, and traffic conditions, leading to complex spatiotemporal dependencies in the data. Recent studies applied deep learning methods to this task and achieved promising results, but challenges persist. The impact of weather is usually overlooked in previous researches. There is also a lack of consideration for capturing the dynamic change of spatial relationships in cities promptly. In this paper, an Attention-based Dynamic Layer-wise Graph Convolution Network (ADLGCN) is proposed to address these issues. Specifically, a cross-attention mechanism based on weather and transportation demand data is presented to quantify the impact of weather on transportation demand. Additionally, a multi-graph convolutional structure is proposed to focus on capturing real-time spatial relationships. A temporal attention mechanism based on multiple historical periods is introduced to capture temporal dependencies in transportation demand. Finally, extensive experiments demonstrate that our model outperforms the state-of-the-art method, with an average improvement in MAE metrics of 4.45% on two real-world datasets.