Cavendish Experiment

The Cavendish Experiment, performed in 1797–1798 by British scientist Henry Cavendish, was alleged to be the first experiment to measure the force of gravity between masses in the laboratory. The results of the experiment were used to determine the masses of the Earth and celestial bodies. The Cavendish Experiment is often held up as evidence for the universal attraction of mass, and as a proof for gravity. The experiment involves two spherical lead balls attached to a torsion balance, which is alleged to detect the faint gravitational attraction between the masses.

When institutions have reproduced this experiment with modern methods involving lasers and instruments of the highest precision, however, the detection of gravity has been fraught with difficulty, giving erratic results.

The use of this experiment as demonstration of the universal attraction of mass is further faulted at its premise. This experiment is a matter of observation and interpretation. A sight attraction with the force equivalent of a few cells is observed and conclusions are deduced. Those observations are used to determine the mass of the earth and the celestial bodies, rather than the theory of gravity and the size of the earth being used to determine the amount of attraction which should be seen. It is assumed that the attraction seen must originate from the universal attraction of mass rather than any other cause. Different values seen in the experiment would produce different conclusions for the masses of the earth and celestial bodies.

Gravity Not a Constant
Scientific American provides an assessment of a large number of Cavendish Experiments conducted by prestigious laboratories and institutions and explains that, unlike other fundamental forces in physics, gravity cannot be accurately measured.

Puzzling Measurement of "Big G" Gravitational Constant Ignites Debate (Archive)

Measuring the Very Faint
Physicist Jens Gundlach explains that gravity is very hard to measure and would require measuring the force equivalent of the weight of a few human cells on two one-kilogram masses that are one meter apart:

Gundlach explains that there are many effects that could overwhelm the gravitational effects. Static attraction, air viscosity, air particles, static drag, other forces, &c, can easily overcome such gravitational attraction.

Wildly Erratic
The article explains that the results are wildly erratic.

The values of these sophisticated laboratory experiments differ from one another by as much as 450 ppm of the gravitational constant. The weight of a few cells as compared to the masses involved in the experiments, what they should be measuring, for context, is smaller than 450 ppm. The uncertainty for measuring the gravity of the opposite mass with the equipment should be only about 40 ppm, yet the values observed are far more erratic—over ten times their estimated uncertainties. It is quite curious that the strength of gravity of the universe would increase or decrease by over ten fold when tested at different times.

450ppm is not accurate. The effect from gravity is a small portion of that. The results need to be consistent to pinpoint any particular phenomenon. As stated, there are plenty of forces and effects stronger than the weak gravity that it might be detecting. If identical experiments cannot replicate results, then it is invalid as a test to demonstrate any one particular cause. Consistency is of prime importance to empirical science. One cannot merely assume that the experiment is detecting a multitude of admittedly stronger effects to cause the inconsistent results, but that gravity is in there somewhere.

While the ranges discussed are small, so too are those forces which modify the results. Plenty of effects could attract with the "force equivalent of the weight of a few cells". Whatever effects one can imagine is modifying the results could also be creating them as well. One quickly sees the consternation of the matter: The 'weight of a few cells' can be caused entirely by a mechanism which is not gravity. The experiments need to be accurate and consistent for a valid test of a particular phenomenon.

A range of forces which causes a faint short range attraction is hardly demonstrable as the gravitational attraction of mass. Cavendish observed the level of g in this short range attraction experiment in the attempt to determine the mass of the Earth. The value was not predicted beforehand. The observed result of the experiment is used to predict the masses of the bodies in the solar system -- an observation to create theory rather than a theory to predict observation. An argument that any attraction seen, of whatever level, must be gravity, is hence fallacious.

Cannot Be Measured
The end sentence is plain in its understanding, and tactfully admits that they cannot measure gravity.

Forbes Article
From a Forbes piece titled Scientists Admit, Embarrassingly, We Don't Know How Strong The Force Of Gravity Is (2018) (Archive) by Dr. Ethan Siegel we read the following about the issue:

This article tells us that, compared to other fundamental constants, the uncertainties with G are thousands to billions of times greater.

Gravity 'Oscillates'
Due to the mysterious readings and problems, some are now calling gravity part of "Dark Energy."

https://www.newscientist.com/article/dn24180-strength-of-gravity-shifts-and-this-time-its-serious/ (Archive)

History
According to physicist George T. Gillies the difficulties in measuring G has been a recurring theme in the study of gravity.

The Newtonian gravitational constant: recent measurements and related studies (1996) (Archive) George T. Gillies

Abstract:

Concluding Remarks - p.212

The Newtonian Gravitational Constant: An Index of Measurements (1983) (Archive) George T. Gillies

Introduction - p.1

Addendum
As suggested by the references above; until physics is able to isolate the gravitational interaction between laboratory masses to the point where other disturbing forces do not dominate the measurement, the Cavendish Experiment should be regarded for what it is: An inconsistent experiment which is admittedly disturbed by unknown or unmitigated effects, and which might or might not include "gravity" in the results seen.

Further, the entire matter is an observation which is used to determine the mass of the Earth and the celestial bodies, as opposed to using the theory of gravity to create a prediction for the strength of the attraction which should be seen. The first paragraph in the Wikipedia article for the Cavendish Experiment says:

We see that the experiment was used to determine the 'constant' and the mass of the earth. The fact that there is attraction of some level in this short range experiment is quite fallacious to utilize as evidence for the universal attraction of mass. The strength of the attraction in the observation merely tells the experimenter what the strength of g would be for the earth and celestial bodies according to conventional theory, provided that the theory and mechanism is correct. There is a lack of demonstration that the cause is actually through the universal attraction of mass. The universal attraction of mass is only assumed.

If we were to feel a gust of wind through an open window, should we assume that the wind was caused by any one particular cause according to one particular theory? Plenty of things can cause wind, and there are also plenty of forces which can attract, especially at the sensitive levels discussed. Measuring the strength of a gust of wind to determine something about the strength or dynamics of a theory about the weather would tell us only about that theory and little about whether the wind seen was actually related to that theory or not. Measuring the strength of a short-range attraction experiment to decide the mass of the earth and celestial bodies would likewise tell us little about the ultimate cause for that attraction, and would serve only to give a little more insight to theory.

A found attraction somewhere around the force equivalent of the weight of a few cells is considered by popular thought to be an impeachable proof for gravity and the universal attraction of mass. Anything which seems to support it does support it, no matter how imprecise, no matter how many other effect may be involved, and the absurdity of equivocating the detection of such a slight effect to one cause above any other possibility in nature is put out of mind and ignored entirely. It is through such inherent fallacy that one hypothesis is built upon the next, in unending succession. Deductions and conclusions are given for a model based on a result, but the foundations remain essentially undemonstrated. It is deemed sufficient to observe and interpret rather than to prove and demonstrate.

Proof by Contradiction
As a proof by contradiction, similar experiments which have attempted measure "gravity" at larger scales than the Cavendish Experiment have been unable to detect gravitational influence. See Variations in Gravity