At this time the Gravitational Constant is regarded as a constant with problematic/low accuracy by physicists. From University of Washington Big G Measurement:
Since Cavendish first measured Newton's Gravitational constant 200 years ago, "Big G" remains one of the most elusive constants in physics. The value of big G tells us how much gravitational force acts between two masses separated by a known distance. In Einstein's language of general relativity, it tells us the amount of space-time curvature due to a given mass. Together with Planck's constant and the speed of light it is considered to be one of the most fundamental constants in nature. Big G is a necessary ingredient in determining the mass of the earth, the moon, the sun and the other planets.
Several measurements in the past decade did not succeed in improving our knowledge of big G's value. To the contrary, the variation between different measurements forced the CODATA committee, which determines the internationally accepted standard values, to increase the uncertainty from 0.013% for the value quoted in 1987 to the twelve times larger uncertainty of 0.15% for the 1998 "official" value. This situation is an embarrassment to modern physics, considering that the intrinsic strength of electromagnetism, for instance, is known 2.5 million times more precisely and is steadily being improved. (The situation of G becomes more understandable if one considers the weakness of gravity: the total gravitational force twisting on the pendulum of a typical Cavendish torsion balance is only equivalent to the weight of a bacteria and that small force must be measured very precisely.)
Since we are talking about physics, this is true to the best of our current understanding.
The question of how/why do we know that G (and other constants) are indeed constant was addressed in Physics.SE: What is the proof that the universal constants (G, ℏ, …) are really constant in time and space?
Regarding the claim that the data isn't made public. I couldn't find any evidence that labs are constantly remeasuring and updating G and I couldn't find that this data is hidden. The data is made public through journal articles. Also, the value is not updated constantly as the National Institute of Standards and Technology published a figure that was last updated at 2010.
Here are 4 different values for G from different sources:
When plotted in a graph with error bars, we have the following:
So measurements are not constantly done, the "official" value is not updated regularly, and the results of the measurements are published.