This study delineates the evolution of magnetic order in epitaxial films of the room-temperature multiferroic BiFeO3 system. Using angle- and temperature-dependent dichroic measurements and spectromicroscopy, we have observed that the antiferromagnetic order in the model multiferroic BiFeO3 evolves systematically as a function of thickness and strain. Lattice-mismatch-induced strain is found to break the easy-plane magnetic symmetry of the bulk and leads to an easy axis of magnetization which can be controlled through strain. Understanding the evolution of magnetic structure and how to manipulate the magnetism in this model multiferroic has significant implications for utilization of such magnetoelectric materials in future applications.