  We study the weak-field limit of the conformal Weyl gravity suggested by
Mannheim as an alternative to Einstein's General Relativity modeling both dark
matter and dark energy. We solve the field equations of the theory in the
weak-field approximation for an arbitrary spherically symmetric static
distribution of matter in the physical gauge with constant scalar field.
Analysing the obtained solution, we conclude that the conformal theory of
gravitaty is inconsistent with the Solar-system observational data.
