The fact that gravimeters read a stronger downward pull (by a needle and a spring sensitive to 0.001 G's) at the top of a mountain (where there is most mass underneath) and low gravity at inverse locations on the Earth, should be compelling evidence that the Earth's mass is responsible for its own local gravity.
There's also the fact that mining companies use this method to detect karsts and voids beneath the surface, where they may contain natural gas and oil. Gravimetric prospecting is very effective, and provides very accurate readings of things such as salt domes. People have been using this method for decades, below are some diagrams from work published in 1944. Just to demonstrate how accurate their readings were, despite only having access to very simple instruments.
This second diagram shows calculations based on their gravimeter analysis with the observed cross section of the salt dome. Given that the real profile of the dome was not known prior to the prediction, and the prediction was very accurate. Not perfect, but very good.
Citation
Barton, Donald C.. "Case Histories and Quantitative Calculations in Gravimetric Prospecting." Pet. Technol. 7 (1944): 1–49. doi:
https://doi.org/10.2118/944111-GWe must conclude that the mass of the Earth beneath our feet is responsible for the downward force that keeps us from floating in zero G.
It's a very simple model, more mass/greater density = more gravity. It is easily testable, measurable, predictable, and is applied in real life to make a lot of people a lot of money for a very long time.
If Celestial Bodies were responsible for gravitational anomalies, then the fact that gravimetric analysis finds what it expects to find (ie. in the above, an accurate profile of the Nash Salt Dome) it would have to be attributed to coincidence! Furthermore, gravimetric analysis should not be repeatable, if their results were coincidence or attributed to celestial objects (given that they are moving relative to our position).