Unfortunately, making understanding the real world is not easily reducible to propositional logic. Since you seem interested in pedantry, the technical thing to say is that you must use Bayesian inference and reasonable priors.

In this case, explanations for A and C being correlated without A causing C are strongly related to explanations for why A and B might be correlated without A causing B. (E.g., people who get married are predisposed to be successful.) Evidence, which necessarily can't be in the form of a randomized controlled experiment and yet can still be very strong, that A in fact causes B greatly reduces ones belief that A might not be causing C. My previous comment was asking whether you would defend alternatives that I find to be very unlikely, like a hypothetical predisposition for people to both get married and be happy but which is completely independent from the increase in earnings.

Since we're talking about belief rather than what we can prove, I think it's extremely plausible for the causation in question to go the other way. Given the choice, would you rather date / marry someone who was happy and healthy or someone who was depressed and drinks too much?

All science is about belief. Randomized controlled trials are useful not because they convey mathematical proof, but because they give strong evidence for beliefs.

Your question doesn't help. For the sake of argument we have granted that marriage causes men to earn more money. And yet, I would still prefer to marry someone who was earning more money (or who had the potential to earn more in the future), all else being equal. This preference doesn't dispute the causation.