Commercially available gravimeters and seismometers can be used for measuring Earth’s acceleration at resolution levels in the order of ng∕Hz (where g represents earth’s gravity) but they are typically high-cost and bulky. In this work the design of a bulk micromachined MEMS device exploiting non-linear buckling behaviour is described, aiming for ng∕Hz resolution by maximising mechanical and capacitive sensitivity. High mechanical sensitivity is obtained through low structural stiffness. Near-zero stiffness is achieved through geometric design and large deformation into a region where the mechanism is statically balanced or neutrally stable. Moreover, the device has an integrated capacitive comb transducer and makes use of a high-resolution impedance readout ASIC. The sensitivity from displacement to a change in capacitance was maximised within the design and process boundaries given, by making use of a trench isolation technique and exploiting the large-displacement behaviour of the device. The measurement results demonstrate that the resonance frequency can be tuned from 8.7 Hz–18.7 Hz, depending on the process parameters and the tilt of the device. In this system, which combines an integrated capacitive transducer with a sensitivity of 2.55 aF/nm and an impedance readout chip, the theoretically achievable system resolution equals 17.02 ng∕Hz. The small size of the device and the use of integrated readout electronics allow for a wide range of practical applications for data collection aimed at the internet of things.