I once heard #1 years ago in yeshiva, but it makes no sense. #2 makes sense- it’s one covering, and it protects your head from sweat.
Siman 90 in the shulchan aruch says that one should keep one’s head covered while davening. Siman 2 in the shulchan aruch says one should always keep his head covered. The Igros Moshe says that as long as your head isn’t “not covered”, then it’s covered. In other words, there is no minimum shiur for yarmulke. Some recent poskim say that the Igros moshe would admit that by davening, the head covering should cover most of a person’s head. The Mishna Brurah brings down the Chayei Adam that nowadays when we wear a hat in the street, we should wear one for davening. The Taz says that one should be “meutaf” in his tallis, ie completely wrapped in it, with his head covered by it. This is brought down by the Shlah and other kabbalah-oriented sources. We are mikayeim the Taz by Shma and shemonah esrei when we cover our heads with the Tallis.
In sum, 3 reasons to cover one’s head:
1. The rule that one should have his head covered by davening
2. The rule that one should wear a hat
3. The rule that one’s head should be covered in a tallis.
Two layers instead of one on a yarmulke has no bearing on any of the other 2 halachos. So I’ll go with “yeshivish shtus”. i heard it too. But it doesn’t pass the “sources” muster.