  Given a partition ${\mathcal V}=(V_1, \ldots,V_m)$ of the vertex set of a
graph $G$, an {\em independent transversal} (IT) is an independent set in $G$
that contains one vertex from each $V_i$. A {\em fractional IT} is a
non-negative real valued function on $V(G)$ that represents each part with
total weight at least $1$, and belongs as a vector to the convex hull of the
incidence vectors of independent sets in the graph. It is known that if the
domination number of the graph induced on the union of every $k$ parts $V_i$ is
at least $k$, then there is a fractional IT. We prove a weighted version of
this result. This is a special case of a general conjecture, on the weighted
version of a duality phenomenon, between independence and domination in pairs
of graphs.
