If your rifle is a Weatherby Accumark, it came with a Krieger (cut rifled) from the factory. If it's a Mark V it came with a Criterion (button-rifled).
Krieger makes excellent barrels, so does Dan Lilja.
Talking with my smith today, he was telling me about some customers he has had that he put cheap Douglas barrels on that the customers say are shooting lights out, and winning, or placing top 3 in 1K comps. He also said that, not to be bragging and in his opinion, a gun will only shoot as good as the skills of the smith who built it. That over the last 60 years he's installed everything from the highest quality to the lowest quality, and that he's seen cheap barrels win tournaments, and good ones lose. So, basically he was saying it's 50% the smith, 40% shooter, and 10% parts.