Vertically stacked van der Waals (vdW) heterostructures not only provide a promising platform in terms of band alignment, but also constitute fertile ground for fundamental science and attract tremendous practical interest towards their use in various device applications. Beyond most two-dimensional (2D) materials, which are intrinsically non-magnetic, CrI is a novel material with magnetism dependent on its vdW-bonded layers, promising potential spintronics applications. However, for particular device applications, a heterostructure is commonly fabricated and it is necessary to examine the effect of the interface or contact atoms on the magnetic properties of the heterostructure. Most importantly, the effect of assembly stress on the electronic and magnetic properties remains unclear. In this study, we design a vdW heterostructure from two-chromium tri-halides, namely the CrI/BrCrI heterostructure, where the Janus equivalent of the CrI monolayer, BrCrI, is also an intrinsically magnetic 2D material. Using state-of-the-art first-principles calculations, we uncover the effects of the contact atoms, as well as external pressure, on the electronic and magnetic properties of the CrI/BrCrI heterostructure. It is found that the heterostructure transitions from an antiferromagnetic (AFM) to ferromagnetic (FM) ground state with pressure larger than certain threshold. We also investigate the magneto-crystalline anisotropy energy (MAE) of the CrI/BrCrI heterostructure. Remarkably, it is found that the MAE is significantly influenced by both the stacking and the contact atoms, varying abruptly and inconsistently with the contact atoms and external pressure. Further, we also reveal a correlation between the MAE and the polar angle. The pressure-regulated magnetic properties of the CrI/BrCrI heterostructure as revealed in this study highlight its potential applications in spintronic devices.