This article presents the notion of the continuous case of the weighted Tsallis extropy function as an information measure that follows the framework of continuous distribution. We introduce this concept from two perspectives, depending on the extropy and weighted Tsallis entropy. Various examples to illustrate the two perspectives of the weighted Tsallis extropy by examining a few of its characteristics are presented. Some features and stochastic orders of those measures, including the maximum value, are introduced. An alternative depiction of the proposed models concerning the hazard rate function is provided. Furthermore, the order statistics of the weighted Tsallis extropy and their lower bounds are considered. Moreover, the bivariate Tsallis extropy and its weighted version are derived. Non-parametric estimators are also derived for the new measures under cancer-related fatalities in the European Union countries data. Additionally, a pattern recognition comparison between Tsallis extropy and weighted Tsallis extropy is presented.