Religion apparently makes people happier. Is that evidence for the truth of religion, or against it?

(Of course, it matters which religion we're talking about, but let's just stick with theism generally.)

My initial inclination was to interpret this as evidence against theism, in the sense that it weakens the evidence for theism. Here's why:

1. As all Bayesians know, a piece of information F is evidence for an hypothesis H to the degree that F depends on H. If F can happen just as easily without H as with it, then F is not evidence for H. The more likely we are to find F in a world without H, the weaker F is as evidence for H.
2. Here, F is "Theism makes people happier." H is "Theism is true."
3. The fact of widespread theism is evidence for H. The strength of this evidence depends on how likely such belief would be if H were false.
4. As people are more likely to do something if it makes them happy, people are more likely to be theists given F.
5. Thus F opens up a way for people to be theists even if H is false.
6. It therefore weakens the evidence of widespread theism for the truth of H.
7. Therefore, F should decrease one's confidence in H, i.e., it is evidence against H.

We could also put this in mathematical terms, where F represents an increase in the prior probability of our encountering the evidence. Since that prior is a denominator in Bayes' equation, a bigger one means a smaller posterior probability--in other words, weaker evidence.

OK, so that was my first thought.

But then I had second thoughts: Perhaps the evidence points the other way? If we reframe the finding as "Atheism causes unhappiness," or posit that contrarians (such as atheists) are dispositionally unhappy, does that change the sign of the evidence?

Obviously, I am confused. What's going on here?