Magnetic control of molecular emission holds the promise of developing new magneto-optical technologies. Spin dynamics of radical pairs can serve as a basis of control of chemical reactions by weak magnetic fields (<1 T) orders of magnitude smaller than the thermal energy kBT at room temperature. Here we demonstrate control of recombination fluorescence, produced by charge recombination of photogenerated radical pairs, by weak magnetic fields in rigid donor-bridge-acceptor molecules excited with visible light. We can tune the field response range by chemically modulating the energies of the radical pairs affecting exchange interactions. Our results present a new strategy for designing magneto-optical probes for imaging and other molecular spin technology applications.