The Op mentioned 400 yards range, and 30-06 is their max recoil tolerance. Most factory rifles with a 3-9x40 scope will get into the 8-8.5lb range and perform well to 400 yards in a variety of calibers, although slightly larger scope would be preferred for 400 yards for my eyes. For example, a Browning X-Bolt Stainless Stalker comes in at 6.5lbs in 308, and adding scope and rings should be able to get in the 8lb range and meet the range and recoil constraints listed.
I echo most others' advice of 7.5-9.5 lbs range. My 8lb rifle gets carried the most, unless I'm in an area of long range shot opportunities then I pack the 9.5lb gun with the larger scope. I wouldn't want to pack an 11lb or 12lb rifle around for long.