Why do we call really late at night the “wee morning hours”?
First of all, the word “wee” suggests a size. Time has no size. It has a duration. “Wee” could apply to the size of a man’s penis, but not to the time he can sustain an erection (assuming no drugs).
I stayed up late one night and timed the “wee morning hours”. They were just as long as all the other hours, including the hour it takes to explain to my wife why her new black blouse is now orange and black and will make a great Halloween costume.
“I stayed up until the early morning hours and now I’m dog tired.”
That suffices as a description, thank you.