I'm learning Italian as well, so my interpretation of the first word is based solely on my own knowledge of language in general (I'm advanced in French speaking).
The first "Di" seems to be what pulls the "quanto" into the sentence in a way that actually makes sense. Rather than saying "How much taller are you," which would make perfect sense in English, you are saying "BY how much" asking more for a specific amount. I translated the sentence as "By how much are you taller than him," which, though much more formal, seems to bring all of the Italian words into the translation in a way that makes sense and is easier to understand. Italian sentences are not pieced together the same way as English or even French, so I find that using this method to learn sentence structure really helps me figure things out.
I hope I was of use!