Accurate prediction of water quality and quantity is crucial for sustainable development and human well-being. However, existing data-driven methods often suffer from spatial biases in model performance due to heterogeneous data, limited observations, and noisy sensor data. To overcome these challenges, we propose Fair-Graph, a novel graph-based recurrent neural network that leverages interrelated knowledge from multiple rivers to predict water flow and temperature within large-scale stream networks. Additionally, we introduce node-specific graph masks for information aggregation and adaptation to enhance prediction over heterogeneous river segments. To reduce performance disparities across river segments, we introduce a centralized coordination strategy that adjusts training priorities for segments. We evaluate the prediction of water temperature within the Delaware River Basin, and the prediction of streamflow using simulated data from U.S. National Water Model in the Houston River network. The results showcase improvements in predictive performance and highlight the proposed model's ability to maintain spatial fairness over different river segments.