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 $\mathcal P_{n,u}$.