  We discuss a model-independent estimator of the likelihood of the
compositeness of a shallow S-wave bound or virtual state. The approach is based
on an extension of Weinberg's relations in Phys. Rev. 137, B672 (1965) and it
relies only on the proximity of the energy of the state to the two-hadron
threshold to which it significantly couples. The scheme only makes use of the
experimental scattering length and the effective range low energy parameters,
and it is shown to be fully consistent for predominantly molecular hadrons. As
explicit applications, we analyse the case of the deuteron, the $^1{\rm S}_0$
nucleon-nucleon virtual state and the exotic $D^{\ast}_{s0}(2317)^\pm$, and
find strong support to the molecular interpretation in all cases. Results are
less conclusive for the $D^{\ast}_{s0}(2317)^\pm$, since the binding energy of
this state is significantly higher than that of the deuteron, and the approach
employed here is at the limit of its applicability. We also qualitatively
address the case of the recently discovered $T_{cc}^+$ state, within the
isospin limit to avoid the complexity of the very close thresholds $D^0D^{\ast
+}$ and $D^+D^{\ast 0}$, which could mask the ingredients of the approach
proposed in this work.
