  We study the equations of conformal gravity, as given by Mannheim, in the
weak field limit, so that a linear approximation is adequate. Specializing to
static fields with spherical symmetry, we obtain a second-order equation for
one of the metric functions. We obtain the Green function for this equation,
and represent the metric function in the form of integrals over the source.
Near a compact source such as the Sun the solution no longer has Schwarzschild
form. We conclude that a solution of Mannheim type cannot exist for these field
equations.
