  In this paper, we continue our study of blade arrangements and the
positroidal subdivisions which are induced by them on $\Delta_{k,n}$. A blade
is a tropical hypersurface which is generated by a system of $n$ affine simple
roots of type $SL_n$ that enjoys a cyclic symmetry. When placed at the center
of a simplex, a blade induces a decomposition into $n$ maximal cells which are
known as Pitman-Stanley polytopes.
  We introduce a complex $(B_{k,n},\partial)$ of weighted blade arrangements
and we prove that the positive tropical Grassmannian surjects onto the top
component of the complex, such that the induced weights on blades in the faces
$\Delta_{2,n-(k-2)}$ of $\Delta_{k,n}$ are (1) nonnegative and (2) their
support is weakly separated.
  We finally introduce a hierarchy of elementary weighted blade arrangements
for all hypersimplices which is minimally closed under the boundary maps
$\partial$, and apply our result to classify up to isomorphism type all rays of
the positive tropical Grassmannian $\text{Trop}_+ G(3,n)$ for $n\le 9$.
