Currently, deep learning-based methods for remote sensing pansharpening have advanced rapidly. However, many existing methods struggle to fully leverage feature heterogeneity and redundancy, thereby limiting their effectiveness. To address these challenges across two key dimensions, we introduce a general adaptive dual-level weighting mechanism (ADWM), designed to enhance a wide range of existing deep-learning methods. First, Intra-Feature Weighting (IFW) evaluates correlations among channels within each feature and selectively weighs to reduce redundancy and enhance unique information. Second, Cross-Feature Weighting (CFW) adjusts contributions across layers based on inter-layer correlations, refining the final output by preserving key distinctions across feature depths. This dual-level weighting is efficiently implemented through our proposed Correlation-Aware Covariance Weighting (CACW), which generates weights by utilizing the correlations captured within the covariance matrix. Extensive experiments demonstrate the superior performance of ADWM compared to recent state-of-the-art (SOTA) methods. Furthermore, we validate the effectiveness of our approach through generality experiments, ablation studies, comparison experiments, and detailed visual analysis.