Joe,
Unlike Acer, I AM opinionated and reserve the right to be the only person who thinks my way.
In my opinion, since you asked, if you want a rifle to target-shoot off-hand and have difficulties with heavy rifles then get a rifle with a looooong swamped barrel that meets your weight criteria. The average stock with lock, etc. will add about 3 pounds to the barrel weight, unless its one of Acer's "chubby-guns".
For a rifle to hold steady you need angular momentum. Momentum is mass multiplied by lever-arm. (Ike Newton worked all this out.) So, for a given weight, a long skinny rifle will develop greater angular momentum because of the longer lever-arm. To compare two different options multiply barrel weight by barrel length. That will give you a rough estimate of the relative angular momenta of the two different barrels AS LONG AS THEY HAVE THE SAME PROFILE. If you are comparing swamped barrels this will work too.
You can build a good handling rifle with a short and heavy barrel but you will sacrifice stability over a rifle of the same weight with a longer barrel. You can build a rifle a light rifle with either a short or long barrel but the one with the longer barrel will be inherently "steadier" when shot off-hand. A swamped barrel will give you far better balance for the same weight and a lighter barrel for the same degree of stability.
That's my opinion. There are a bunch of folks that think I'm nuts. That's their right.
Best Regards,
John Cholin