The aim of the present paper is to investigate the weighted relative extremal functions and weighted capacities with weights in the Cegrell classes $\mathcal{F}$ and $\mathcal{E}$. Some results on the connection between the weighted capacities with the weighted relative extremal functions are established. Moreover, we give a characterization of weighted capacities $C_{n,u}$ through $u$ and prove the absolute continuity of $C_{n,u}$ with respect to the Sadullaev’s weighted capacity ${\mathcal{P}}_{n,u}$.