Breaking the time-reversal symmetry (TRS) in topological insulators (TIs) through ferromagnetic doping is an essential prerequisite for unlocking novel physical phenomena and exploring potential device applications. Here, we report the successful growth of high-quality (DyxBi1-x)2Te3 thin films with Dy concentrations up to x = 0.355 by molecular beam epitaxy. Bulk-sensitive magnetisation studies using superconducting quantum interference device magnetometry find paramagnetic behaviour down to 2 K for the entire doping series. The effective magnetic moment, μeff, is strongly doping concentration-dependent and reduces from ∼12.6 μB Dy-1 for x = 0.023 to ∼4.3 μB Dy-1 for x = 0.355. X-ray absorption spectra and x-ray magnetic circular dichroism (XMCD) at the Dy M4,5 edge are employed to provide a deeper insight into the magnetic nature of the Dy3+-doped films. XMCD, measured in surface-sensitive total-electron-yield detection, gives μeff = 4.2 μB Dy-1. The large measured moments make Dy-doped films interesting TI systems in which the TRS may be broken via the proximity effect due to an adjacent ferromagnetic insulator.