  We introduce the resource quantifier of weight of resource for convex quantum
resource theories of states with arbitrary resources. We show that it captures
the advantage that a resourceful state offers over all possible free states, in
the operational task of exclusion of subchannels. Furthermore, we introduce
information-theoretic quantities related to exclusion and find a connection
between the weight of resource of a state, and the exclusion-type information
of ensembles it can generate. These results provide support to a recent
conjecture made in the context of convex quantum resource theories of
measurements, about the existence of a weight-exclusion correspondence whenever
there is a robustness-discrimination one. The results found in this article
apply to the resource theory of entanglement, in which the weight of resource
is known as the best-separable approximation or Lewenstein-Sanpera
decomposition, introduced in 1998. Consequently, the results found here provide
an operational interpretation to this 21 year-old entanglement quantifier.
