Your post has drawn out a lot of suspect advice.
1) Let's not address the relative value of lightness in a rifle, I'll assume you understand the shootability trade-offs you'll be making, and feel the juice is worth the squeeze. These trade-offs come not only in the form of increased recoil but also in reduction of features (vertical grip, negative comb, flat toe, etc) which accrue to performance. I'll also assume you understand the importance of shooting smaller cartridges in such ultralight rifles.
2) Now assuming lightness is your only goal, and your rifle-only budget is $2600, the most shootable ultralight setup would be a $500 Howa Mini barreled action in 6 ARC placed in a $450 Stocky's VG carbon stock with $150 Jefferson Outdoor bottom metal. That'll keep you around 5 pounds and change once you throw on a rail and rings.
3) In the used market, NULAs and gen 1 Barrett Fieldcrafts are prized for a reason. Neither are made anymore in any configuration worth buying.
4) If you are willing to accept slightly more weight, a Tikka action in a carbon stock with a short threaded shorter barrel can be configured bare to well under 6 pounds before optics. Unlike the others, this will not be a functional compromise but merely a recoil energy compromise. Both this option and the Howa Mini option will leave you with a spare grand and change to spend on optics, suppression, and
ammo (which are arguably more important).
Best,
-J
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