Diamagnetic levitation is a promising technique for realizing resonant sensors and energy harvesters since it offers thermal and mechanical isolation from the environment at zero power. To advance the application of diamagnetically levitating resonators, it is important to characterize their dynamics in the presence of both magnetic and gravitational fields. Here we experimentally actuate and measure rigid body modes of a diamagnetically levitating graphite plate. We numerically calculate the magnetic field and determine the influence of magnetic force on the resonance frequencies of the levitating plate. By analyzing damping mechanisms, we conclude that eddy current damping dominates dissipation in mm-sized plates. We use finite element simulations to model eddy current damping and find close agreement with experimental results. We also study the size-dependent Q-factors (Qs) of diamagnetically levitating plates and show that Qs above 100 million are theoretically attainable by reducing the size of the diamagnetic resonator down to microscale, making these systems of interest for next generation low-noise resonant sensors and oscillators.