I have never tried to add weight to a stock - do you have an actual number that you want to add, or just until it "feels right"? My only similar experience was my one and only attempt to stiffen a floppy plastic stock - I laid in hollow carbon fibre arrow shafts to the forearm and anchored with epoxy. Sort of worked, but not really - the stock had a lot of "hinge action" through the magazine area, so really needed something along the magazine up into the fore end to "stiffen" it. Was just not enough room in there for an arrow shaft. Might be an issue for you, but I do not know - adding weight to the forearm and to the butt stock will definitely help to soak up recoil, I think, but any weight up front might be stressing the magazine area??? I have a pre-64 Win M70 and a Rem 30 - both in 30-06 - they have apparatus that ties the forearm to the barrel - do not commonly see that - so in most rifles, the barrel might want to rise and leave the weighted fore arm behind???
Your project is more than idle curiosity for me - I have a Zastava 458 Win Mag that weighs 8 pounds 3 ounces - unloaded, without scope - I have never fired it with factory loads - some experienced acquaintances tell me that I would be nuts to try running full house loads through a rifle that light - seems that 10 or 11 pounds plus would be more appropriate. A Win 70 in 375 H&H had a barrel mounted secondary recoil lug - this Zastava does not, so there is that to address as well. So, have been toying with doing all together - a barrel mounted recoil lug, bedded into the forearm, weight added and a screw through the forearm up into that recoil lug...