  We study how the number of degrees of freedom in Weyl conformal gravity runs
with the energy scale from the UV fixed point. To this end we employ two
approaches. First, we utilize the Fradkin--Tseytlin prescription for the number
of degrees of freedom and demonstrate that the one-loop results are highly
dependent on the selected background. We then employ the counting methodology
based on the $a$- and $c$-functions, which are typically used to characterize
the trace anomaly of conformal field theory in four dimensions. We compute
these in the enhanced one-loop approximation and demonstrate that the degrees
of freedom decrease monotonically from six degrees in the UV regime. This
behavior is independent of the backgrounds considered. Finally, we show how to
relate the Fradkin--Tseytlin prescription to counting based on the $a$- and
$c$-functions.
