i became acquainted with weird al when i was a teenager. he sure did make fun of stuff good. over the years i have come to know of his musical/comedic genius.
i dont know if its because of the timing of him releasing material, or what, but my youngest brothers(19 and 21) both discovered weird al in their young teenage years, as well. i dont think they really appreciate him/his work like most of us do, but still.
I wonder if there's a generation gap here. I mean, I grew up listening to Weird Al, too, and I love it in part because it makes me laugh and in part because it makes me feel like a kid again. But I wonder if you had to be there. I wonder if you had to "know him when" he was just trying to get his tapes on Dr. Demento to truly appreciate the story of a class clown growing up to live the dream of getting millions of dollars just to be goofy and make people laugh.
The thing that amazes me about Al is that he really can emulate any musical style. He makes it look effortless, too. I can't find the interview now, but I remember reading that he really struggled with the lyrics for his parody of Lose Yourself because he wanted to make it sound as good as the original, but Eminem's rhymes were so tightly structured that it really challenged him as a writer*.
I don't know if you can "mature" into liking Weird Al. I think perhaps you have to be the kind of person who listened to him when you were still immature, and to be willing to let yourself devolve a bit to truly enjoy it.
*Edited due to memory fail.