There are 2 schools of thought on that. A lot of guys like to match a compact lightweight rifle with a compact lightweight scope. And depending on the way it is meant to be used that can be a good plan.
On the other hand going to a lighter weight rifle allows you to use a heavier scope and still reduce the amount of weight you're carrying.
With a modern rifle 6 lbs 12 oz isn't considered lightweight anymore, anything over 7 lbs is heavy. There are lots of rifles closer to 6 lbs and some closer to 5 lbs. My Kimber with an 11 oz scope on it is still under 6 lbs scoped. You'll be very close to 8 lbs, maybe over 8 lbs depending on the mounts you choose.
For me it depends on the specific rifle and scope. I don't mind carrying extra weight if I feel I'm getting something in return. I'd feel better about giving more specific advice if I knew which rifle, and which scope you had in mind and the planned uses.