  In this paper, we study the weakly weighted Einstein-Finsler metrics. First,
we show that weakly weighted Einstein-Kropina metrics must be of isotropic
S-curvature with respect to the Busemann-Hausdorff volume form under a certain
condition about the weight constants. Then we characterize weakly weighted
Einstein-Kropina metrics completely via their navigation expressions or via
$\alpha$ and $\beta$ respectively.
