I have no center fires that are 6 pounds and lighter. I do have a few that are just a few ounces over 6 pounds however. Here is my lightest rifle. A 1900 Lee in 303 with a very light barrel, but as light is it is, it still shoots as well as I can from a rest with the iron sights it has. 100 yard groups hold a smidgen under 2MOA.
(If that's not good enough please keep quite about it ----------so the deer I have been killing with it WON'T KNOW it's not good enough to kill them. So far they don't seem to know that---------)