I think GSP's a great champion and a great ambassador for the sport. He's also imo the most dominant welterweight champion in history.
That being said, I think Anderson Silva would beat him. This is mma anything can happen (although GSP takes NO risks), but I'm pretty sure Anderson would win 98% of the time.
As for the GSP can beat light-heavyweights and heavyweights at a UFC level argument. We just saw GSP come off a lackluster performance and his supporters turn around and say he can beat lightheavyweights/heavyweights? Lol, get a hold of yourselves.