The impact of interfacial electronic reconstruction on the magnetic characteristics of La0.7Sr0.3CoO3 (LSCO)/La0.7Sr0.3MnO3 (LSMO) heterostructures was investigated as a function of layer thickness using a combination of soft x-ray magnetic spectroscopy and bulk magnetometry. We found that the magnetic properties of the LSCO layers are impacted by two competing electronic interactions occurring at the LSCO/substrate and LSMO/LSCO interfaces. For thin LSCO layers (<5 nm), the heterostructures exist in a highly coupled state where the chemically distinct layers behave as a single magnetic compound with magnetically active Co2+ ions. As the LSCO thickness increases, a high coercivity LSCO layer develops which biases a low coercivity layer, which is composed not only of the LSMO layer but also an interfacial LSCO layer. These results suggest an intriguing route to tune the magnetic properties of transition metal oxide heterostructures through careful control of the interface structure.