In the era of big data, the explosive growth of multi-source heterogeneous data offers many exciting challenges and opportunities for improving the inference of conditional average treatment effects. In this paper, we investigate homogeneous and heterogeneous causal data fusion problems under a general setting that allows for the presence of source-specific covariates. We provide a direct learning framework for integrating multi-source data that separates the treatment effect from other nuisance functions, and achieves double robustness against certain misspecification. To improve estimation precision and stability, we propose a causal information-aware weighting function motivated by theoretical insights from the semiparametric efficiency theory; it assigns larger weights to samples containing more causal information with high interpretability. We introduce a two-step algorithm, the weighted multi-source direct learner, based on constructing a pseudo-outcome and regressing it on covariates under a weighted least square criterion; it offers us a powerful tool for causal data fusion, enjoying the advantages of easy implementation, double robustness and model flexibility. In simulation studies, we demonstrate the effectiveness of our proposed methods in both homogeneous and heterogeneous causal data fusion scenarios.