We report on the magnetic properties of Co clusters grown on Au(111) in the cluster-size range from 300 to 12000 atoms. These clusters are superparamagnetic at room temperature, while at low temperatures blocking of the thermal fluctuations leads to a macroscopic remanence. The hysteresis curves measured in situ by means of x-ray magnetic circular dichroism show that the blocking temperature scales with cluster size, following a finite-size scaling power-law behaviour. We find that the blocking temperature of these clusters is substantially reduced by a thin silver overlayer, indicating a reduction in the perpendicular magnetic anisotropy at low coverages. With this change in anisotropy a clear change in the shift exponent can be observed.