  The observation of hydrodynamic transport in the metallic delafossite
PdCoO$_2$ has increased interest in this family of highly conductive oxides,
but experimental studies so far have mostly been confined to bulk crystals. In
this work, the development of high-quality thin films of PdCoO$_2$ has enabled
a thorough study of the conductivity as a function of film thickness using both
dc transport and time-domain THz spectroscopy. With increasing film thickness
from 12 nm to 102 nm, the residual resistivity decreases and we observe a large
deviation from Matthiessen's rule (DMR) in the temperature dependence of the
resistivity. We find that the complex THz conductivity is well fit by a single
Drude term. We fit the data to extract the spectral weight and scattering rate
simultaneously. The temperature dependence of the Drude scattering rate is
found to be nearly independent of the residual resistivity and cannot be the
primary mechanism for the observed DMR. Rather, we observe large changes in the
spectral weight as a function of disorder, changing by a factor of 1.5 from the
most disordered to least disordered films. We believe this corresponds to a
mass enhancement of $\geq 2$ times the value of the bulk effective mass which
increases with residual disorder. This suggests that the mechanism behind the
DMR observed in dc resistivity is primarily driven by changes in the electron
mass. We discuss the possible origins of this behavior including the
possibility of disorder-enhanced electron-phonon scattering, which can be
systematically tuned by film thickness.
