  The characterization of the gravitational field of isolated objects is still
an open question in quadratic theories of gravity. We study static equilibrium
solutions for a self-gravitating fluid in extensions of General Relativity
including terms quadratic in the Weyl tensor $C_{\mu\nu\rho\sigma}$ and in the
Ricci scalar $R$, as suggested by one-loop corrections to classical gravity. By
the means of a shooting method procedure we link the total gravitational mass
and the strength of the Yukawa corrections associated with the quadratic terms
with the fluid properties at the center. It is shown that the inclusion of the
$C_{\mu\nu\rho\sigma}C^{\mu\nu\rho\sigma}$ coupling in the lagrangian has a
much stronger impact than the $R^2$ correction in the determination of the
radius and of the maximum mass of a compact object. We also suggest that the
ambiguity in the definition of mass in quadratic gravity theories can
conveniently be exploited to detect deviations from standard General
Relativity.
