Let me try again. Not all barrels are great barrels. At a theoretical level, a heavy barrel and a thin barrel may be equally accurate. At the consumer level however, I do believe that the accuracy of a thin barrel is impacted more by barrel quality and quality of the bedding of the rifle. In other words, a standard or heavy barreled rifle with mediocre stock bedding will mask the negative effects of the bedding better than a thin barreled rifle will. That's why I said, and why I believe, that if you want an ultralight rifle you really want a high quality barrel. And, high quality bedding.
As for the original point of this thread - to float or not - I do believe that floated is the way to go, if the rifle is bedded well. Again...back to my Ruger Compact with the short thin barrel. I wanted the barrel floated and I had an extra short-action synthetic Ruger stock (came with my standard barrel Hawkeye). I dropped the action into that synthetic stock and it was instantly floated, but the rifle just didn't shoot worth a darn. Like I've done before with other rifles, I put a lot of reloads through it and tinkered with loads for days and days, trying to find the elusive great load. I couldn't do it. Hmmm, maybe it's the darn stock, since the Hawkeye didn't shoot that great in that same stock. So I put the action back into the original wood stock with barrel pressure points and it shoots great. I have absolutely no doubt that the rifle will shoot at its best in a high dollar well-bedded stock, but that's a lot of money to spend just to shrink the groups by 1/4 of an inch, so I'll leave it as is for now.
And...I do have that short action synthetic Ruger stock for anyone that wants it.