Images captured under low light conditions are often affected by intense noise, which may become more pronounced during image enhancement, resulting in poor visual quality. The aim of this paper is to establish an effective low-light image enhancement model that can suppress noise and artifacts while preserving image details. To deal with intense noise, we propose a Weighted Low-Rank Tensor regularization Retinex (WLRT-Retinex) model, which introduces weighted low-rank tensor priors in the Retinex decomposition process to suppress noise and artifacts in the reflectance. Furthermore, since noise in dark areas is typically more severe, we introduce an illumination-aware weighting scheme in the total variation regularization term of the reflectance, which helps achieve adaptive denoising and preserve details in bright areas. Experiments on seven challenging datasets demonstrate the effectiveness of the proposed method, achieving better or comparable performance compared with state-of-the-art methods. Our code is available at https://github.com/YangWeipengscut/WLRT-Retinex.