Atom interferometers have demonstrated a high sensitivity to inertial forces. This enables their application in gravimetry, creating a new type of instrument for continuous absolute gravity measurements. The Gravimetric Atom Interferometer (GAIN, Humboldt-Universität Berlin) is a mobile atom interferometer based on interfering ensembles of laser-cooled Rb-87 atoms in an atomic fountain configuration. It has been specifically designed for on-site measurements of the absolute value of g as well as continuous recordings. High precision applications in geodesy and geophysics, e.g. land uplift near the zero-line, require terrestrial gravimetric measurements with an accuracy of a few tens of a nm/s² and even lower. Currently, these tasks are performed by classical free-fall absolute (AG) and superconducting gravimeters (SG). The operation of both types of instruments is to some degree interdependent, because AGs are used for SG calibration and drift determination, and SG measurements can improve AG measurements for environmental effects and provide observed tidal parameters. As SGs are operated continuously recording over extended periods of time, they are also used to determine the long term stability of AGs and identify offsets after repairs or upgrades. Atom interferometers potentially combine the applications of AG and SG by drift-free recording of absolute g. We present the current state of the development of GAIN and the advances made between two campaigns at the geodetic observatories in Wettzell, Germany, in 2013 and Onsala, Sweden, in 2015. Comparisons with the SG and the FG5X-220 show the improvement of precision and of absolute accuracy. GAIN values agree with the FG5X-220 ones at the level of 50-60nm/s². The RMS of the difference of GAIN and OSG-54 measurements in Onsala is 5nm/s^2 at an averaging time of 30 minutes.