My varmint gun is pretty heavy. Wood stock, big, extendable Harris bi-pod and huge 8.5-25x scope. It's not bull-barrel though. The weight never bothered me. We used to walk a perimeter that a couple hundred feet elevation and about a 3 mile circuit. I was never bothered.
On bull versus sporter or some such, it's really a barrel quality issue. Quality barrels without internal defects (stresses) don't change POI as they heat up.
I go with what I like in terms of looks and never worried much about the rest.
Here's my semi-custom Savage. It's a deer gun first and varmint second. My pure varmint gun is a bone-stock and scary accurate Ruger M77 MkII.
