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 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, as the attraction seen in the experiment is used to determine the mass of the earth and the celestial bodies instead of the theory of gravity and the size of the earth being used to determine the amount of attraction which should be seen. Different values would produce different conclusions for the masses of the earth and celestial bodies. It is assumed that the attraction seen must originate from the universal attraction of mass rather than any other cause.

Gravity Not a Constant
You 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.

450ppm is not accurate. The effect from gravity is a small portion of that. The results need to be consistent, and they need to match gravity. As stated, there are plenty of forces and effects stronger than the weak gravity that it might be detecting.

If it cannot replicate the results which identical experiments are seeing, then it is invalid as a test to demonstrate any one particular cause. Consistency is of prime importance to emperical 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.

Whatever effects one can imagine is modifying the results could also be creating them as well. One quickly sees that the experiments need to be accurate and consistent for a valid test of a particular phenomenon.

A range of forces which causes short range attraction of some level 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 (Archive) by Dr. Ethan Siegel we read the following about the issue:

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 tthe mass of the Earth and the celestial bodies, rather than using the theory of gravity to create a prediction for 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'. The fact that there is attraction of some level in this short range experiment is 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 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 any particular theory? Plenty of things can cause wind, and there are plenty of forces which can attract. 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 little about whether the wind seen was 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. Such assumption does not follow. It is through such assumption and 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 undemonstrated. It is deemed suffient to interpret rather than to prove.

As a proof by contradiction, experiments at larger scales are unable to detect "gravity." See Variations in Gravity