High performance tunable absorbers for terahertz (THz) frequencies will be crucial in advancing applications such as single-pixel imaging and spectroscopy. Metamaterials provide many new possibilities for manipulating electromagnetic waves at the subwavelength scale. Due to the limited response of natural materials to terahertz radiation, metamaterials in this frequency band are of particular interest. The realization of a high-performance tunable (THz) absorber based on microelectromechanical system (MEMS) is challenging, primarily due to the severe mismatch between the actuation range of most MEMS (on the order of 1-10 microns) and THz wavelengths on the order of 100-1000 microns. Based on a metamaterial design that has an electromagnetic response that is extremely position sensitive, we combine meta-atoms with suspended at membranes that can be driven electrostatically. This is demonstrated by using near-field coupling of the meta-atoms to create a substantial change in the resonant frequency. The devices created in this manner are among the best-performing tunable THz absorbers demonstrated to date, with an ultrathin device thickness (1/50 of the working wavelength), absorption varying between 60% and 80% in the initial state when the membranes remain suspended, and with a fast switching speed (27 us). In the snap-down state, the resonance shifts by γ>200% of the linewidth (14% of the initial resonance frequency), and the absorption modulation measured at the initial resonance can reach 65%.