<p>In this paper, we utilize a weight function g to regulate the pace of the statistical convergence in a topological space. We extend the notion of statistical convergence to weighted statistical convergence by utilizing the weighted density. Using this intriguing idea of convergence, a new variation of γ-covers (referred to as s<sub>g</sub>-γ cover) is introduced. Subsequently some topological analysis are conducted on the class of s<sub>g</sub>-γ coverings. It is demonstrated that the new class of s<sub>g</sub>-γ coverings lies some where between the class of γ-covers and the class of s-γ cover classes.</p>
