Changes in the spin configuration of atomically thin, magnetic van der Waals multilayers can cause drastic modifications in their opto-electronic properties. Conversely, the opto-electronic response of these systems provides information about the magnetic state, which is very difficult to obtain otherwise. Here, we show that in CrCl3 multilayers, the dependence of the tunnelling conductance on applied magnetic field, temperature and number of layers tracks the evolution of the magnetic state, enabling the magnetic phase diagram to be determined experimentally. Besides a high-field spin-flip transition occurring for all thicknesses, the in-plane magnetoconductance exhibits an even-odd effect due to a low-field spin-flop transition. Through a quantitative analysis of the phenomena, we determine the interlayer exchange coupling as well as the layer magnetization and show that in CrCl3 shape anisotropy dominates. Our results reveal the rich behaviour of atomically thin layered antiferromagnets with weak magnetic anisotropy.