  The weak-binding relation is a useful tool to study the internal structure of
hadrons from the observable quantities. We introduce the range correction in
the weak-binding relation for the system having a sizable magnitude of the
effective range, and show that the applicability of the weak-binding relation
can be enlarged by the range correction. Thanks to the low-energy universality,
the weak-binding relation can be used to study the structure of shallow bound
states in any systems with different length scales. We apply the weak-binding
relation to actual systems, including hadrons, hypernuclei, and atoms and show
the importance of the range correction.
