  We present a combinatorial monomial basis (or, more precisely, a family of
monomial bases) in every finite-dimensional irreducible
$\mathfrak{so}_{2n+1}$-module. These bases are in many ways similar to the FFLV
bases for types $A$ and $C$. They are also defined combinatorially via sums
over Dyck paths in certain triangular grids. Our sums, however, involve weights
depending on the length of the corresponding root. Accordingly, our bases also
induce bases in certain degenerations of the modules but these degenerations
are obtained not from the filtration by PBW degree but by a weighted version
thereof.

Representation Theory;Combinatorics