I just picked up a CZ 527 .223 Varmint. It's a heavy barrel, though I agree that it's not what I would call a bull barrel. It's certainly heavier than a slim hunting barrel, but it's not quite as heavy as some. I think the length of the barrel is as much of a factor, as the barrel is quite long. I actually haven't gotten to fire it yet, so I'm hoping it's a good shooter.
It really doesn't feel that heavy compared to my much shorter Howa 1500, with a "sporter" barrel profile, though I haven't weighed them to compare.
The 527 American has a shorter barrel and a lighter profile. The two 527 American rifles I looked at in the store did not seem to be truly free-floated barrels. Both had very little gap between the barrel and stock, and both had at least one point with slight contact. My varmint model has good clearance and is floated all the way to the action. May not be a big deal to you, but something to keep in mind.