Cost him twice as much, with the added benefit that it gives the person the right to mention their double major twice in every sentence they speak/write.

I think they mean that chose to major in <X>, with music as a second (additional) major.

I can only presume, but I believe they meant they graduated with a 'main' major (possibly something technical, like engineering or CS, since we're in HN), but also double majored (i.e. also majored) in music.