Guess I'll take the opposing view on this.
Using my heavy varmint rifle (17 pounds) and my light varmint rifle (8.5 pounds) and shooting both from a bench with a rest, bench with bags, bench with bipod, and prone with bipod, there is no difference, POA to POI in any of these methods.
The light rifle is in a factory Remington synthetic sporter stock, and the heavy gun is in a factory Remington BDL wood stock.
Impact changes are primarily addressed via the way the shooter holds the rifle, which tends to change with differing support methods.
It's all about consistancy guys, hold it the same, it'll shoot the same.