  In this paper, we investigate the boundedness, compactness, essential norm
and the Schatten class of weighted composition operators $uC_\varphi$ on
Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in
H(D): uC_\varphi:A_\omega^p\to A_\omega^p \mbox{ is bounded}\}.$ For some
regular weights $\omega$, we obtain that $X=H^\infty$ if and only if $\varphi$
is a finite Blaschke product.
