Lot's of opinions that it's the
skin on your elbow--when I was a kid 30 years ago, however, it quite clearly was used as a combo-word in between "Wussy and Penis."
So if you weren't quite a Wussy (
Weiner/Pussy), and you were kind of acting like a
dick, you were a Weenis/Weenus.
"
Dude, stop being such a Weenis! You talked
us into
climbing up here, so you get to jump first."