When selecting features for knowledge discovery applications, stability is a highly desired property. By stability of feature selection, here it means that the feature selection outcomes vary only insignificantly if the respective data change slightly. Several stable feature selection methods have been proposed, but only with empirical evaluation of the stability. In this paper, we aim at providing a try to give an analysis for the stability of our ensemble feature weighting algorithm. As an example, a feature weighting method based on L2-regularized logistic loss and its ensembles using linear aggregation is introduced. Moreover, the detailed analysis for uniform stability and rotation invariance of the ensemble feature weighting method is presented. Additionally, some experiments were conducted using real-world microarray data sets. Results show that the proposed ensemble feature weighting methods preserved stability property while performing satisfactory classification. In most cases, at least one of them actually provided better or similar tradeoff between stability and classification when compared with other methods designed for boosting the stability.