Network-aware cascade size prediction aims to predict the final reposted number of user-generated information via modeling the propagation process in social networks. Estimating the user's reposting probability by social influence, namely state activation plays an important role in the information diffusion process. Therefore, Graph Neural Networks (GNN), which can simulate the information interaction between nodes, has been proved as an effective scheme to handle this prediction task. However, existing studies including GNN-based models usually neglect a vital factor of user's preference which influences the state activation deeply. To that end, we propose a novel framework to promote cascade size prediction by enhancing the user preference modeling according to three stages, i.e., preference topics generation, preference shift modeling, and social influence activation. Our end-to-end method makes the user activating process of information diffusion more adaptive and accurate. Extensive experiments on two large-scale real-world datasets have clearly demonstrated the effectiveness of our proposed model compared to state-of-the-art baselines.