In recent years, the study of variability in uncertainty measures has gained significant interest in information theory. In this context, the concept of varextropy has been introduced and investigated by several researchers. This paper focuses on the study of weighted varextropy and introduces weighted residual varextropy, presenting a thorough examination of their theoretical properties. Specifically, we investigate the impact of monotonic transformations on these measures and derive various bounds. Additionally, we analyze the application of weighted varextropy within coherent systems and proportional hazard rates models. A non-parametric kernel-based method is introduced to estimate weighted (residual) varextropy, and the estimators' consistency and asymptotic normality are given. Finally, the effectiveness of this estimation method is demonstrated through simulations as well as analysis of a real-world data set, illustrating its potential applications in uncertainty analysis
