A little is all it takes to justify not accepting a miracle as true.

Extraordinary claims require extraordinary evidence or hard evidence at least. We are not saying miracles need miraculous evidence - we will settle for very strong evidence.

If something is beyond outrageous, you are justified in disbelieving it happened - even if your reason is a small one. For example, if the evidence points to the local statue of Jesus committing murders you can disbelieve in this on the grounds that there is no wear and tear on his feet. You can conclude then that he is not taking secret excursions. It is reasonable to take this approach instead of trying to surmise that maybe the statue moves around by levitation and its feet are never touching the ground.

What if there is incredibly good evidence for a miracle and one weak piece of evidence that it may not be a miracle?

A lot of people think feeling bad at a miracle report is enough to justify dismissing it. A person should feel bad if Annie is cured of a limp while little Johnny is left to die in agony. Of course you should feel happy for Annie but you must feel strongly and badly for Johnny. To be happy about such discrimination indicates, "Great! There is a supernatural power! I hope it can look after me!" That increases the vulgarity. You could say that the bad feeling is a sign from God not to believe for the feeling is a gift.