The measurement of the gravitational acceleration through light-pulse atom interferometers is a current topic for matter-wave based inertial sensing. Such interferometers have been developted in analogy to optical Mach-Zehnder interferometers, where beam splitters and mirrors are realized by diffracting light pulses. In this contribution, we will present two types of tunneling-based gravimeters: The first one resembles an optical Fabry-Pérot interferometer. The matter-wave cavity is described by two Gaussian barriers, so that reflection and transmission are determined by the tunneling effect instead of diffraction. In the first configuration, we study the effect of gravity on the transmission through the cavity. For the second gravimeter, we prepare the effective ground state of the cavity and consider the asymmetry during the time-evolution due to the tunneling process.