Another problem with some centerfire scopes with large objectives and power over, say 6X, is that they need to be focused for closer shooting. The smaller the objective, the less light-gathering power, but the greater the need for focusing at short range.
I have several scopes on rimfires in the 4-14X power range, which have adjustable objectives, but they're big and heavy and need to be focused more than scopes with lower power and smaller objectives. When walking around with them, I keep the power to a minimum and set the objective to about 30-40 yards, so if I see a rabbit or other small game, it will be in focus.
In the past, I've used a trick to minimize focus and parallax problems on centerfire scopes used for target shooting. It involves cutting a "donut" of thin black cardboard, with the outside diameter the size of the objective lens and the hole about 2/3 rds the size of the objective. A little electrical tape holds the disk in place.
Because light rays don't need to bend as much nearer the center, there's less need for precise focus and parallax correction. There is some loss of brightness, but that doesn't matter much on the shooting range. Try it, you might like it.
If I can't be with the rifle I love, I love the rifle I'm with!!