Correlation and Causation

I know, of course, that causation cannot be inferred from correlation. The question is whether causation can be ruled out (not with certainty, but with probability) based on a correlation that is not as high as expected. I will use an example that was previously posted on the site to explain.
Some claim a correlation between education and apostasy. If I show, for example, that the correlation between high socioeconomic status and apostasy is much stronger, and there is a correlation between education and socioeconomic status, then it is more likely that the causality is socioeconomic status and the correlation with education is explained as being because socioeconomic status is related to both.
In other words, because we found that the correlation is weaker than what is seen in other correlations and can be explained without causality, we can say that it is unlikely that there is causality here.
B. I ask this because as part of my research I examine correlations between the expression of different genes in different cells, and when examining tens of thousands of genes there are thousands of correlations, and one has to separate the wheat from the chaff. The question is whether there are existing models that you know of that are able to predict which correlations can represent causation with a high probability and which are less likely because they can be explained based on other, stronger correlations. I would be happy if you could contact me for more information on the subject.
(By the way, thanks for the recent columns on causality)