I have 3 blr 81's and like them very much. But, they have always seemed a little muzzle light or butt heavy. Is there any way to correct this problem without doing something radicaal like rebarreling ?

I hear ya. What I did was core out the stock. This made it receiver heavy, which is still better than stock heavy.

I also dremeled a bit of aluminum out of the receiver. It lightened up a bit, but I wouldn't recommend doing it.

I wish they would make the blr with a heavier contour barrel even if it added a few ounces.