We report the thickness dependence of Dzyaloshinskii-Moriya interaction (DMI) and spin-orbit torques (SOTs) in PtCo(t)AlOx, studied by current-induced domain wall (DW) motion and second-harmonic experiments. From the DW motion study, a monotonous decay of the effective DMI strength with an increasing Co thickness is observed, in agreement with a DMI originating at the PtCo interface. The study of the ferromagnetic thickness dependence of spin-orbit torques reveals a more complex behavior. The effective SOT-field driving the DW motion is found to initially increase and then saturate with an increasing ferromagnetic thickness, while the effective SOT-fields acting on a saturated magnetic state exhibit a non-monotonic behavior with increasing Co-thickness. The observed thickness dependence suggests the spin-Hall effect in Pt as the main origin of the SOTs, with the measured SOT amplitudes resulting from the interplay between the varying thickness and the transverse spin diffusion length of the Co layer.