  We consider the problem of finding a basis of a matroid with weight exactly
equal to a given target. Here weights can be discrete values from
$\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such
discrete values. We resolve the parameterized complexity completely, by
presenting an FPT algorithm parameterized by $\Delta$ and $m$ for arbitrary
matroids. Prior to our work, no such algorithms were known even when weights
are in $\{0,1\}$, or arbitrary $\Delta$ and $m=1$. Our main technical
contributions are new proximity and sensitivity bounds for matroid problems,
independent of the number of elements. These bounds imply FPT algorithms via
matroid intersection.
