The genius of Weird Al is that he doesn't just write a funny song that has the same melody as the original. It also has the same rhyme structure, and much of the time uses the same phonemes. He parodies specific lines from the original, twists them, and again rhymes them the same way, resulting in numerous "punch lines" throughout the song. Sometimes the parody song has nothing to do with the original ("The Saga Begins" <--> "American Pie") but often, as with this example ("You're Beautiful" <--> "You're Pitiful") he directly attacks the original.
And best of all, he's gotten better at making his version just plain sound like the original. Production sounds similar, instruments have basically the same sound, even his voice somehow sounds "Bluntish" here, or maybe it's just the way he sings. Probably both.
I have every Weird Al album, in full, on my iPod. I don't care that the idiots at AMG say his target audience is 13-year-old boys; I think the guy's a true genius and I love his work.