Sometimes there is
What you really need in an accurate 22 is a match-grade chamber, regardless of the barrel profile. Standard 10/22 chambers are quite loose inside so that they may work reliably with many types of ammo. However, a match, or "Bentz", chamber is much tighter, and doen't feed all cheap ammo well. This of course means that the bullet doesn't have room to wiggle and it presses more tightly into the rifling, and thus performs better. The problem with a tight chamber is that if you chamber a standard hi-velocity round in it, often the only way to remove the round is by firing the gun, whereas in a standard chamber, you could just manually work the bolt and eject it yourself. Most heavy barrels come standard with match chambers, which is a major part of why heavy barrels are accurate. There are, BTW, some companies making standard weight barrels for the 10/22 with match chambers. Also, there are some heavy barrels designed with non-match barrels so that people can use popular ammo like CCI Stingers. In fact, Green Mountain makes a standard barrel available with either a specially cut Stinger chamber, or Bentz chamber, and you make your choice when ordering. The chamber is one of the most important aspects of accuracy -- far moreso than barrel weight
As for the heavy profile, some people say that the heavy barrel is stiffer and more accurate, but many of the worlds most accurate 22s use non-heavy barrels including CZ, Remington 541T, Anschutz, Cooper, Sako, etc.
As for using a heavy barrel with an alluminum action, yes it does stress the action due to its weight, so many people don't free-float heavy-barrelled 10/22s. Futhermore, since the 10/22 uses a press-fit barrel, you are always going to fight barrel alignment, especially with a heavy barrel. For that reason, many companies make 10/22 actions out of steel, and include a threaded barrel hole instead of the press-fit layout.
If you are really looking for an accurate 22, the Ruger 10/22 needs so much work, whereas many others, like a CZ Lux for example, provides competition-grade accuracy out of the box, even with its very thin barrel. Likewise, a Thompson Center 22 Classic often outshoots even heavy-barrelled 10/22s using its sporter-weight barrel.
This is all first hand information. I own or have owned countless 22s, including several 10/22s complete with heavy barrels. I hope this helps!