That's a very nice point! This is a solid way to debunk the flat earth. "Celestial gravitation" is almost as poor a response as "i can draw a diagonal line on a side view and that = perspective". Absolutely no way to account for differences due to direction when the same "celestial objects" are above you in both directions.
I'm thinking a very nice way to measure this is the shanghai maglev: that puppy gets up to 430km/h and travels in a nearly perfect west/east direction and very straight in the mid section (i.e. where it's going 430)... and it's a very short distance so pretty cheap for someone to buy a few trips both ways and bring a scale with them
Plus the "east" track is right next to the "west" track so no other reason for deviation. Some rudimentary math based on that Wiki graph, a 10kg mass should weigh about 15grams more travelling east, and 15 grams less travelling west: i think that's easily measurable on cheap equipment? Hell you could always just use your phone's accelerometer (not sure if accurate enough?)
Went on that train last year: FYI it's awesome lol Was thinking there'd be some mention of Eötvös effect in relation to it but can't immediately find it on web: guaranteed they factored that in to the engineering! I wonder if they adjust the mag lev strength "up" accordingly or just use a flat rate and doesn't matter if it rides higher/lower hmm