I don't think there is much doubt that,all things being equal, a heavy barrel will group with repeat shots more "accurately" than a light tube....but a few sessions of schlepping a heavy rifle in rough country, or where game can appear at any time and the rifle will be (should be) in your hands most of the day,gets real old, real quick.Cruising bedding areas for mule deer in rough country comes to mind and for that work,a heavy barrel just sucks IMO....
I like to mix up the criteria for a rifle,and watch very carefully where it puts the first one, from a cold barrel,every time,and do this over the course of a year,and at distances from 300-600 yards,and from different rests and conditions....oh I shoot for groups, too,and like Mule Deer will once in a great while just sit and shoot 8-10 shots because this will really show flaws in the rifle if any exist...cant prove it with math,but know that flaws in the rifle will show up with 5-10 shot groups that may not be apparent with 3 shot groups.But I sure don't do this every session an once a rifle shows it groups well,I rarely, if ever just it down and shot a bunch of groups from the bench.
But once that stuff is out of the way,I revert back to cold barrel POI consistency,and what the rifle and I do with it in my hands...by then I "know" the rifle,and it reaches "boring" status..and by the time it gets boring,it's ready to hunt.
This is as easy to accomplish with a light tube as a heavy one for hunting purposes,and I consider it more important than pure grouping ability because it is very rarely that I get to kill an animal with a "group",which is the way I like things to turn out....like Rick points out,if you botch the firt one,things generally are on a downward spiral from there on out,and redemption is hard to achieve.
