While there are theoretical advantages to a heavy barrel, there are no actual inherent accuracy advantages. An accurate barrel is an accurate barrel, be it light or heavy, and I have seen many instances where a light-barrel rifle outshot the same model of rifle with a heavy barrel. Without doubt, a heavy barrel is stiffer, and this can be an advantage -- or not. It also heats up more slowly, which can mean better accuracy over long shot strings -- or not. Unless a hunting rifle is going to be used for something like prairie dogs, where long shot strings can occur, or used exclusively from stands, I'll opt for an accurate light barrel any day simply for ease of carry.

I will also say that in 50 years of rifle-tinkering I have seen at least as many tackdrivers turned in to mediocre shooters by the "usual mods" as mediocre shooters turned in to tackdrivers. Relatively simple and inexpensive trigger mods and load development usually produce just as much accuracy improvement as a full-house job.