Steven Scott Statistician is a firm believer in the Bayesian method of testing a hypothesis and is interested in all matters mathematical regarding proving and disproving theories. He has written many papers on the topic. The Bayesian method in a simplistic nutshell states that to get two matches when repeating the same test proves a theory. The method has had some criticism, but you can see the logic in the approach. The first person to come up with the theory was Reverend Thomas Bayes a British Reverend who had the idea but soon abandoned it. It was then looked at by Pierre Simon Laplace who gave it its modern day feel and interpretation.
However, the first point to take into consideration is that you can never truly prove a theory, that is how the world of Maths and Science work, you can never categorically say without a shadow of a doubt that you are one hundred percent right.
Sometimes like the gravity theory it is an explanation that we give to it makes sense. If we throw a ball one hundred times it will fall one hundred times. What we do not know is whether the detailed description that we give of why this happens, which is that objects accelerate towards each other when they are otherwise left to their own devices, is the actual reason. We may need to eliminate other effects or set up control situations to test our theory further. For example what will happen if the same tests are carried out in a vacuum; also, can we show that this will happen irrespective of what the mass is; to test this we must use all kinds of objects of varying shapes and sizes.
So, your theory is initially considered the best and most straightforward way to explain what is happening and you have done lots and lots of testing that supports this hypothesis. There is nothing already known or in the realms of nature that counteracts what you are saying, then yay you have demonstrated that you might have a theory or explanation! But that is as good as it gets.
Thus we know that this is a scientifically and universally accepted theory but it is only a theory, in the case of the gravity theory we are probably at the point of it being an established theory and this occurs when any attempts to disprove it fail and if this happens and continues to happen all over the world then the best that you can hope for is that your theory gets accepted and promoted to an established theory. This is time to party!
The problem is that there is no way to categorically state that there isn’t something else causing the articles to fall; that there isn’t some other phenomenon taking place that we know nothing about. Because we can’t disprove everything or anything else, then we cannot prove our theory and again this is how science and maths work.