  This note is devoted to the study of Hyt\"{o}nen's extrapolation theorem of
compactness on weighted Lebesgue spaces. Two criteria of compactness of linear
operators in the two-weight setting are obtained. As applications, we obtain
two-weight compactness of commutators of Calder\'{o}n--Zygmund operators,
fractional integrals and bilinear Calder\'{o}n--Zygmund operators.
