Following the recent isolation of monolayer CrI3 (ref. 1), many more two-dimensional van der Waals magnetic materials have been isolated2,3,4,5,6,7,8,9,10,11,12. Their incorporation in van der Waals heterostructures offers a new platform for spintronics5,6,7,8,9, proximity magnetism13 and quantum spin liquids14. A primary question in this field is how exfoliating crystals to the few-layer limit influences their magnetism. Studies of CrI3 have shown a different magnetic ground state for ultrathin exfoliated films1,5,6 compared with the bulk, but the origin is not yet understood. Here, we use electron tunnelling through few-layer crystals of the layered antiferromagnetic insulator CrCl3 to probe its magnetic order and find a tenfold enhancement of the interlayer exchange compared with bulk crystals. Moreover, temperature- and polarization-dependent Raman spectroscopy reveals that the crystallographic phase transition of bulk crystals does not occur in exfoliated films. This results in a different low-temperature stacking order and, we hypothesize, increased interlayer exchange. Our study provides insight into the connection between stacking order and interlayer interactions in two-dimensional magnets, which may be relevant for correlating stacking faults and mechanical deformations with the magnetic ground states of other more exotic layered magnets such as RuCl3 (ref. 14).