It's difficult finding a Les Paul Custom that weighs under 10lbs and pretty much impossible to find them under 9 5lbs. The 57 BBs are lighter.Gibson's website states that standard Customs are weight relieved. And boy, they weigh in at eight to nine pounds as it is.
I don't believe historic Customs are weight relieved, though. Of course, without ebony, we may not see them for a while.