We consider the Volterra integral operator $T_{rho,psi}:L_p(0,infty)to L_q(0,infty)$ for $10$. We also obtain similar sharp estimates for the approximation numbers of $T_{rho,psi}$, thus extending former results due to Edmunds et al. and Evans et al..The entropy estimates are applied to investigate the small ball behaviour of weighted Wiener processes $rho W$ in the $L_q(0,infty)$-norm, $1