There is such things as good and bad rings. Additionally, I would never chance using rings designed for an airgun on a high power rifle.
Personally, I am not a fan of Weaver rings/bases, but I do have a couple rifles that still wear them including one of my regularly used deer rifles. Investing in a quality set of rings and bases for a high power rifle is one of the more critical elements, but that doesn't mean you need to spend 100's of $$. If you shop, you should be able to secure a quality set of rings/bases for $50 - $100. I am not familiar with Barrett products...are you considering installing s tactical rail on the rifle? If not, then these rings probably aren't a good choice. You also do NOT need to spend that kind of money for a quality ring. The NcStar rings? No way I would put those on any of my guns...the price says it all!
I have had good luck with Millet, Warne, EGW, DMZ and Redfield and Lupy rings/bases...you can secure a good set of rings/bases from any of these manufacturers for $100 or less...I recommend using a 1 piece base when possible and dovetail type rings/bases. Remember, you will need bases as well as rings.