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. Oddly, modern repetitions of the Cavendish Experiment tell us that the readings deviate over ten fold from their expected uncertainties when observed at different times.1, 2 It is admitted that the experiment is dominated by effects which are not gravity.3, 4

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. In this experiment a slight attraction with the force equivalent of the weight of a few cells is observed 5 and conclusions are then made about the strength of gravity for the entire universe. Those observations are used to estimate the masses of the celestial bodies, rather than using the theory of gravity and the size of the earth to determine the amount of attraction which should have been seen in the experiment. It is assumed that the attraction seen must originate from the universal attraction of mass rather than any other cause which could cause attraction with the weight of a few cells at close range. 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 - Scientific American (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 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 suggested by the source provided that the amount of error makes the experiment inaccurate. As previously 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 may be questionable 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 strengths discussed are small, so too are those forces which modify the results. Plenty of effects could potentially attract with the "force equivalent of the weight of a few cells". One can see that the effects which one can argue or imagine are modifying the results to produce the deviations seen could also be creating them as well. One quickly sees the consternation of physicists involved: The "weight of a few cells" can be caused entirely by a mechanism, or mechanisms, which is not gravity. The experiments would ideally be accurate and consistent for greater confidence in a particular phenomenon.

Cannot Be Measured
The end sentence is plain in its understanding, admitting 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 (Archive) by astrophysicist Ethan Siegel, Ph.D. (bio), we read the following about the issue:

We are told that, compared to other fundamental constants, the uncertainties with G are thousands to billions of times greater. We are also told that the strength of gravity for the celestial bodies across the universe are all reliant on this inconsistent experiment.

The article further repeats that the experiments were seeing ranges which were over ten times the expected uncertainties:

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 and dominated 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 gravity '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 gravity would be for the earth and celestial bodies according to conventional theory, provided that the assumptions are 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 effects and forces which can attract, especially at the slight 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 not about whether the wind seen was actually related to that theory or not. Measuring the strength of a short-range attraction experiment 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. Accordingly, anything which seems to support it does support it, no matter how imprecise, no matter how many other effects may be dominating the results of the experiment, 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 the mind and ignored entirely. It is through such inherent fallacy that one hypothesis is built upon another. Deductions and conclusions are given, but the foundations remain essentially undemonstrated. It is deemed sufficient to observe and interpret rather than to prove and demonstrate.

A Statistical Approach
A common approach to justifying the results of the Cavendish Experiment is to assert that we need only find the closest mean, median, or mode of the results, and to declare that this is the value of 'gravity'. Yet, minimal introspection on this approach will show that finding a statistical average value of the effects which are dominating the experiment would tell us only what the average is for the dominating effects, and not about 'gravity'.

Proof by Contradiction
As a proof by contradiction, similar experiments which have attempted measure gravity at larger scales than the shorter ranges of the Cavendish Experiment have been unable to detect gravitational influence. There is a reason for why the Cavendish Experiment is cited as one of the very few proofs of gravity. It is typically neglected mention in the classroom that a great amount of effort has gone into searching for gravitational variations from either the earth or external bodies, with negative results. See Variations in Gravity and Isostasy