Cavity optomechanical phenomena, such as cooling, amplification, or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compared to amplification in the normal dissipation regime. In addition, we analyze the parametric instability, i.e., optomechanical Brillouin lasing, and contrast it to conventional optomechanical phonon lasing. Finally, we propose an experimental scheme that realizes the reversed dissipation regime using parametric coupling and optomechanical cooling with a second electromagnetic mode enabling quantum-limited amplification. Recent advances in high-Q superconducting microwave resonators make the reversed dissipation regime experimentally realizable.