  In this work, we consider weighted anisotropic Hardy inequalities and trace
Hardy inequalities involving a general Finsler metric. We follow a unifying
approach, by establishing first a sharp interpolation between them, extending
the corresponding nonweighted version, being established recently by a
different approach. Then, passing to bounded domains, we obtain successive
sharp improvements by adding remainder terms involving sharp weights and
optimal constants, resulting in an infinite series-type improvement. The
results extend, into the Finsler context, the earlier known ones within the
Euclidean setting. The generalization of our results to cones is also
discussed.
