The essential norm of weighted composition operators on weighted Banach spaces of analytic functions is computed in terms of the weights and the inducing symbols. As a consequence the boundedness and compactness of these operators is characterized. As another consequence the essential norm of composition operators on weighted Bloch spaces is obtained and, consequently, the boundedness and compactness of composition operators on these spaces is also characterized. Particular instances of weighted Bloch spaces are the Lipschitz spaces. The method used allows a unified treatment of the problem of boundedness and compactness on these spaces.