Thin-walled parts are prone to large machining deformation during milling, which compromises machining quality. Conventional studies are mostly limited to fixed tool-workpiece combinations and rely on simulations or experiments to build single-fidelity surrogate models, which are time-consuming and poor in generalization. To address these issues, this paper proposes a variable-fidelity surrogate modeling method for efficient prediction of machining deformation of thin-walled parts under varying tool conditions. First, finite element simulations are performed to obtain deformation data for a source tool under sufficient milling parameter combinations. A cosine similarity criterion is then applied to select a small set of representative parameter combinations for a target tool and compute the corresponding deformation values. Subsequently, affine transformation together with target-domain data is used to update the source-domain deformation data, reducing the distribution discrepancy between the two domains. Finally, the updated source-domain data and the limited target-domain data serve as low- and high-fidelity information, respectively, which are fused via a collaborative Kriging (Co-Kriging) model to establish a prediction model for machining deformation of thin-walled parts in the target domain with milling parameters as inputs. Experiments are conducted on L-shaped TC4 titanium alloy thin-walled parts using two end mills with different helix angles. Results show that at a labeled sample ratio of 0.4, the proposed method achieves an average mean absolute percentage error of 8.94%, lower than 10.69% obtained by the model using only the labeled target data. Moreover, the prediction accuracy of the proposed model is superior to that of the comparison models based on random selection, without affine transformation, or using transfer learning, demonstrating that the proposed method ensures prediction accuracy while significantly reducing the required sample size for a new tool. This work provides an efficient modeling tool for deformation control of thin-walled structures under varying milling conditions.