  The measurement of the size of gravitationally bounded structures is an
important test of gravity theories. For a given radius different theories can
in fact predict a different gravitational stability mass (GSM) necessary to
ensure the stability of the structure in presence of dark energy. We compute
the GSM of gravitationally bounded structures as a function of the radius for
different scalar-tensor theories, including $f(R)$ and generalized Brans-Dicke,
and compare the theoretical predictions to observational data. Since the GSM
only gives a lower bound, the most stringent constraints come few objects with
a mass lower that the one expected in general relativity. The analysis of
different observational data sets shows that modified gravity theories (MGT)
are compatible with observational data, and in some cases fit the data better
than general relativity (GR), but the latter is not in strong tension with the
observations. The data presently available does not provide a conclusive
evidence of the need of a modification of GR, with the largest deviation of
order $2.6 \,\sigma$ for the galaxy cluster NGC5353/4. Future data from galaxy
surveys such as the Euclid mission could be important to get stronger
constraints.
