I can tell you from experience that heavy rifles suck, but I shoot what I would consider a "normal" rifle and it's not too bad. The lighter the better, but your barrel will heat up faster. If you're wearing gloves it will make it bearable.
I prefer something lighter, it's just more convenient to carry around and shoot (unless you're using a bipod). If you plan to sit & blast a whole bunch of rounds off real fast, the bull barrel would take longer to get hot.
For what I do, I don't need the weight of a bull barrel. Sometimes it will get hot when we're blasting away, but that's what handguards are for.