High-fidelity gaze redirection is critical for generating augmented data to improve the generalization of gaze estimators. 3D Gaussian Splatting (3DGS) models like GazeGaussian represent the state-of-the-art but can struggle with rendering subtle, continuous gaze shifts. In this paper, we propose DiT-Gaze, a framework that enhances 3D gaze redirection models using a novel combination of Diffusion Transformer (DiT), weak supervision across gaze angles, and an orthogonality constraint loss. DiT allows higher-fidelity image synthesis, while our weak supervision strategy using synthetically generated intermediate gaze angles provides a smooth manifold of gaze directions during training. The orthogonality constraint loss mathematically enforces the disentanglement of internal representations for gaze, head pose, and expression. Comprehensive experiments show that DiT-Gaze sets a new state-of-the-art in both perceptual quality and redirection accuracy, reducing the state-of-the-art gaze error by 4.1% to 6.353 degrees, providing a superior method for creating synthetic training data. Our code and models will be made available for the research community to benchmark against.