An incredibly small penis, often smaller than that of an infant's.
Guy 1: "Wow, I heard Henry Sick just got dumped."
Guy 2: "Yeah, his girlfriend was tired of his teenie-weenie. She told me if it was any smaller it'd be a clit."
Guy 1: "Yeah, I always pegged him for having a cock that would make a baby-carrot look like a blimp."
Guy 2: "Me too, I felt really bad for her so naturally I let her slurp my cock-monster as a condolence."
What some of the authors of many of these definitions seem to have.
You can tell when someone has a teenie weenie (or the female equivalent: a shriveled clitoris or yet worse - a shriveled soul!) by the bitterness in their words. Sad.