Here's a look at my modified Ruger 10/22 (aka Ruger AR-14 & 1/2). What you see taped around the hand stock is a lead weight, the same lead weight used in an AR-15 buttstock. It's a weighty piece of lead. I taped it on carefully, with padding between, so as to not scratch the wood. What you can't see is the weight I put into the buttstock. I carefully drilled out a considerable portion of the buttstock and put lead in there. I am in the process of making that part permanent by applying epoxy resin to hold the weight in there. I will make it look nice so it won't detract from the rifle, at least not to me. Although it looks a little redneckishly, suprisingly, it has a similar feel to my AR-15, just a little lighter. While holding it offhand, I experience the same movements I encounter in the service rifle league. I am in the process also of making some targets that simulate what I would see in league shooting at 200 yds. I can see this being a big help to improving offhand shooting. It is about as difficult as league shooting.
I shot well over 100 rds off hand at other targets, at 50ft, then decided to shoot 20 rds, at a similar pace and format as I would in the league. After each shot I lowered the rifle to simulate reloading a single round, then raised the rifle into position again to shoot. One of my shots, about 15rds in, is the poor shot bottom left. I simply had a brain lapse. The black center of the target is similar to the entire scoring portion of the league target, in perception that is. The rest of the shots weren't bad, but the poorer ones are the low left shots. My poorer shots in league are usually low, and left. I'm not sure why I shoot low on offhand, but that is usually where the bad ones end up.
All and all, I feel this will help my offhand shooting, and it's fun in the process.