What caliber do you have?
You can add weight to the rear of the stock and yes the foam is normal. Some people will put in SS rods or whatever else they can get in there and then use epoxy or spray foam to seal it in there and keep it from rattling around. Also you may want to epoxy in some metal in the forend of the stock, this will help stiffen it and add some weight. Just be sure your barrel is free floating when you are done and I would advise doing this since the forend on most of the Savage sythetics is pretty flimsy.
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