The data provided here corresponds to the data presented in Figures 2-5 in the manuscript.The file "ZippedData.zip" consists of all the datasets used to construct the PSD and Allan Deviation plots in Figure 2. Two files are provided for each record -- one corresponding to the raw data and the other corresponding to the data corrected for linear drift. Measurements were carried out at the Cambridge University Nanoscience Centre (labelled by NSC) laboratory and at a seismic vault operated by the BGS in Eskdalemuir (labelled by BGS), Scotland. The files labelled with the wording "........EarthTides.zip" provide the time series data for the plots in Figures 3 and 4 in the manuscript demonstrating the tracking of the response to Earth tides in two different locations. The locations (either BGS or NSC) where measurements have been conducted are provided in the file name. There are two files included for each set one consisting of the raw datafiles including the output frequencies of the two resonators and the differential frequencies, while the other provides the corrected time-stamped gravity readings in microGal. The theoretical values for this period as generated by the software TSoft are also included. The time stamp is referenced to UTC. An excel spreadsheet is provided for the data underlying Figure 5 acquired at the University of Bristol Nanoscience and Quantum Information Lab 2017 Chiapas, Mexico, Earthquake (Mw 8.2) on September 8, 2017. The time-series data (in "g" units) from the MEMS device is provided together with the time-series data from a macroscopic seismometer located in Swindon, UK as part of the BGS monitoring network. An additional file provides the time-series data acquired (timestamp, output frequencies of two resonators, differential frequency, accelerometer output) at NSC on February 16, 2018 corresponding to the 16th February 2018 earthquake in Oaxaca state, Mexico. This dataset is reported in the Supplemental manuscript included with the main paper.