  We examine the viability of Weyl conformal gravity as an alternative to the
general theory of relativity. By using the extended rotation curve of the Milky
Way and velocity dispersions of four globular clusters, we show that Weyl
gravity predictions without resorting to dark matter comply with observations
at the galactic scale. For the Milky Way, we demonstrate that the uncertainty
in baryonic modelling results a bracket of possible rotational velocities which
well encompasses the diversity in rotation curve construction. Such diversity
generally arises from differences in measurements of velocity anisotropy
parameter, and the circular speed and Galactocentric distance of the Sun.
Furthermore, we explore the ability of Weyl gravity to account for the inferred
acceleration of Abell cluster 1689.
