  In two previous works, "compact versions" of Rubio de Francia's weighted
extrapolation theorem were proved, which allow one to extrapolate the
compactness of an linear operator from just one space to the full range of
weighted Lebesgue spaces, where this operator is bounded. In this paper, we
extend these results to the setting of weighted Morrey spaces. As applications,
we easily obtain new results on the weighted compactness of commutators of
Calder\'on--Zygmund singular integrals, rough singular integrals and
Bochner--Riesz multipliers.
