  We establish both sufficient and necessary conditions for weighted Hardy
inequalities in metric spaces in terms of Assouad (co)dimensions. Our
sufficient conditions in the case where the complement is thin are new even in
Euclidean spaces, while in the case of a thick complement we give new
formulations for previously known sufficient conditions which reveal a natural
duality between these two cases. Our necessary conditions are rather
straight-forward generalizations from the unweighted case, but together with
some examples they indicate the essential sharpness of our results. In
addition, we consider the mixed case where the complement may contain both
thick and thin parts.
