The potential of wide-field magneto-optical Kerr microscopy for the characterisation of low-dimensional van-der-Waals crystals is explored using the example of Cr₂Ge₂Te₆ flakes in the ten nanometers thickness range. Although the magnetic domains with an expected width in the hundred-nanometer range cannot be seen on this material due to the limited lateral resolution, we show that Kerr microscopy is nevertheless a very valuable method for measuring the magnetization loops on selectable thickness regions on the flake. From the loop character one can indirectly infer on the existence or suppression of band domains, which are the equilibrium patterns above a film thickness of about 7 nm. We derived this characteristic thickness from the initial susceptibility of the hysteresis loops and used it to estimate the specific domain wall energy to be 2.7·10^-4kJ/m². We further demonstrate a thickness- and light colour dependent sign inversion of the Kerr signal that is explained by a Fresnel-type depth sensitivity concept. Accordingly, the Kerr contrast is governed by the relative phase of the Kerr amplitude that can be freely adjusted by a rotatable compensator. The compensator is thus the decisive optical element in magneto-optical Kerr magnetometry and microscopy on low-dimensional materials. It needs to be appropriately aligned to avoid a cancelation of the Kerr contrast and to maximise the Kerr signal.