It should be very clear to anyone who looks up that Mishana Berura that the reason to wear a hat is that it is Derech Kovod. Nothing to do with the number of coverings. I have seen men put their arm over their yarmulka when making a brocha and I believe it to be a total waste of time. Ditto wearing a smacked up, dusty out of shape hat which you would never wear in front of a king.
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