I built a 7 BC on a very lightweight Tikka build with an 18" carbon fiber wrapped barrel. Whole gun is 7 pounds 6 ounces scoped up. So far no issues with all the factory ammo I've tried. It's favorite so far is the 155 gr TAs going 3126. I am going to reload it with 160 gr Barnes LRX at some point and see how it goes. So far, I am loving the gun and has performed very well for me at the range.
Granted semi-custom versus factory could make a huge difference. A colleague of mine picked up a Seekins PH3 in 7 BC and no issues there either, that one is just heavier.