Per the very slight differences in g, as gauged by gavimetry, at higher altitudes or between different areas, here is a paper about how gravimetry is performed. It's not a direct reading from a device. The results are averaged out over several days, and it is admitted that many different elements affect the device...
"The first absolute gravity measurements in The Netherlands"
https://ncgeo.nl/downloads/50Crombaghs.pdfIn order to be able to compare measurements from different points of time, a number of mass displacements (tides, polar motion, length of day variation) are modelled, and corrected for. Effects like ground water variations and air pressure variations are difficult to model. Therefore it is tried to limit these effects during the gravity measurements, by combining the measurements of several days.
Of course, air pressure is different at the top of a mountain and at sea level, as well as near the poles and the equator. I refer back to the thread we had involving the gnome experiment.
Here we have scientists, talking about absolute gravimeters, saying that air pressure may affect the device,
and that they can't model for it. The other elements listed, such as ground water variations, may also have differences between the top of a mountain and at sea level. Again, things the researchers admit that they are unable to model for.
It's not even a "it may the device." The fact that the reading is an averaging of a statistical output to try and account for the variations tells us all we need to know.