It seems to me that If we approach this without any presumptions, both sides carry equal weight.
Yes, but both sides will never carry equal weight if the the argument for such patterns (that prove or disprove one's beliefs) is approached scientifically, which does require making astute assumptions and predictions (presumptions) about how things will turn out, if the assumptions about why the supposed patterns occur are in fact valid. There have been, for instance studies done on the efficacy of prayer that found it ineffecacious for heart patients, and that found a direct correlation between increased patient deaths in those who knew they were being prayed for.
It is important to understand the difference between scientific evidence and anecdotal evidence: science does make presumptions/assumptions and rigorously tests the assumptions; and if the assumptions are shown true by repeatedly tested evidence, the assumptions are treated as theoretical, scientific fact, until proven wrong by better tests.
This is why germ theory is regarded as a fact - in the same way that evolutionary and other scientific theories are regarded as facts. Nothing more scientific has, nor is likely to disprove them.
Anecdotal "evidence" does not operate in this way. It does not demand double blind studies of the hypotheses; nor does it subject itself to rigorous testing of any sort because This is The Way Of Faith and of anecdotal thought and of the false pattern-identification that is its hallmark.
I suppose all arguments regarding pattern-identification would carry equal weight if not tested scientifically. This is why so many people seem to think that Astrology is scientific. They simply don't understand some very basic scientific principles and they see all arguments as having equal weight because of such flawed thinking.