As a key component in rotating machinery, rolling bearings typically operate at variable speed conditions. However, the inertia resulting from speed variations can generate additional momentum on the bearing, causing sudden vibrations or shocks that are misinterpreted as fault features in the envelope analysis process. Additionally, frequency aliasing and strong noise under variable speed conditions degrade signal quality. These factors interfere with the accurate extraction of fault features. To address this issue, a weak fault feature extraction method considering the inertia effect for rolling bearings under variable speed conditions is proposed. Initially, the angular form of the original vibration signal is obtained through computed order tracking (COT) to preserve essential fault features by aligning the signal to the shaft speed. Subsequently, the maximum correlation envelope robust kurtosis filtering (MCERKF) method is proposed to enhance fault features while mitigating the effects of outliers and noise, with the dung beetle optimizer (DBO) being employed to calculate the critical parameters. Finally, a component selection function considering the shocking, cycle stability, and correlation with the original signal is proposed, using energy share, envelope entropy, and correlation coefficient. An optimal component is selected to further enhance noise robustness based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The proposed method is validated with datasets from Ottawa, Canada, and Xi'an Jiaotong University. Compared with the recently proposed similar methods, it effectively mitigates the impact of inertial effects and demonstrates excellent anti-noise performance.