It sounds like you think that I'm denying that g varies relating to latitude/altitude in the predicted way but I'm not. I was looking for experiments because I couldn't find any. So thank you for providing some academic examples, but a more compelling experiment would be one that almost anyone can do and that is well documented in a visual way, which should be the goal. So for instance someone could take a scale to some mountain and, after controlling for temperature and humidity, measure the weight of some thing and see if it matches the prediction. People can understand that experiment instead of expecting them to understand based on their limited understanding of atomic clocks and advanced gravimetry devices or whatever. Not to mention that an experiment that can be performed by only a few with extraordinary means ought to be distrusted on principle.
The issue you are always going to have is that the changes in g that we experience, either by changing our position on the earth’s surface, or by changing our height, are generally very small indeed. You therefore need very accurate devices to be able to show the changes. This either means very precise scales / balances, or more advanced stuff like gravimeters. Your best bet would be to measure a solid object near where you live using very accurate scales and then travel closer to the equator , at the same elevation above sea level, somewhere and measure the same object again using the same scales. If your scales are accurate to the order of <0.1% then you should see some discernible change.
This is a bit easier, I would suggest, than changing your elevation, where the changes are smaller and the confounding factors, such as pressure, are more apparent. It’s also quite difficult for most people to ascend to an altitude high enough to make a measurable difference, and using an aircraft brings with it all sorts of other errors.
I’m still curious to understand, if you generally accept the idea that g does vary with height, but remain convinced that the earth is flat, what do you suppose is going on? What do you think gravity is?