Cavity optomechanics, which utilizes the interaction between light and mechanical motion has been extremely successful in detecting and controlling the mechanical motion with high sensitivities. To improve the coupling between light and mechanical motion, several implementation have been adapted both in microwave and in optical domain of light. The combination of low mass density, high frequency and high quality factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force/mass sensing and exploring the quantum regime of mechanical motion. By coupling a high quality-factor multilayer graphene mechanical resonator to a superconducting microwave cavity, we achieve a displacement sensitivity of 17 fm-Hz-0.5. The large optomechanical coupling is further demonstrated by observing effects such as optomechanically induced transparency, microwave-mechanical gain of 17 dB, and a cooperativity of 8, which is promising for the quantum regime of graphene motion. In a new implementation of an optomechanical setup based on a SiN membrane resonator and a 3-dimensional superconducting microwave cavity. We achieve a cooperativity C of 146,000. Utilizing the sideband cooling technique, we cool a large 123 kHz mechanical resonator down to an occupancy of 5.2 phonons, corresponding to a mode temperature of 34 micro-Kelvin. This new implementation has the potential of reaching the elusive single-photon strong coupling regime.