  We give two weighted norm estimates for higher order commutator of classical
operators such as singular integral and fractional type operators, between
weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey
spaces. We also give the optimal parameters involved with these results, where
the optimality is understood in the sense that the parameters defining the
corresponding spaces belong to certain region out of which the classes of
weights are satisfied by trivial weights. We also exhibit pairs of non-trivial
weights in the optimal region satisfying the conditions required. Finally, we
exhibit an extrapolation result that allows us to obtain boundedness results of
the type described above in the variable setting and for a great variety of
operators, by starting from analogous inequalities in the classical context. In
order to get this result we prove a Calder\'on-Scott type inequality with
weights that connects adequately the spaces involved.
