Some tuner designs use additional weight. How much, where, what material, etc. is subject to considerable debate. There is some argument that longer barrels might respond better to tuners in general (more flex to begin with).
Some tuner designs - like Cortina's original version - add no weight, at least in the original design. It was designed around a 1.250"straight cylinder 32" barrel on an F-Open rifle, and when machined and installed correctly, you had to look pretty close to even tell there was one installed at all - the tuner was literally the same diameter as the barrel contour. Therefore, you were only adjusting the position of the weight at the end of the barrel, not adding any weight to the gun (since unlike PRS, F-class guns do have weight limits that are enforced at the bigger matches). That was literally the big draw to the Cortina tuner originally - that it *didn't* add an extra 4-6 oz of weight to the gun.
When people started using them on FTR guns, where the weight limits are even tighter, and a 30" heavy Palma or heavy Varmint contour about as much as you can get away with even with aluminum or titanium actions, rings, etc. you started seeing the same 1.250" diameter tuner, but tapered down to match the barrel contour. Some of that is offset by the material that is removed from the muzzle for the install process. So they did add some weight - not a lot, but some. Maybe a couple ounces. Doesn't sound like much, but in any sport with rules some people gotta ride the razor's edge.
But to the question as to whether initially adding weight helps/matters - I think sometimes it does. I've had a barrel or three over the years that shot lights out with a brake, or a suppressor installed, but with a bare muzzle they shot like crap (or at best, 'meh').
Typically you find there is at least one spot somewhere in one revolution (as mentioned above, maybe 50 thou of travel) that is noticeably better - and they do tend to repeat. Generally I do my load development with the tuner bottomed out at '0', and then once everything is as good as I can get it thru normal means, I take that load and start playing with the tuner. I think *one* time I actually ended up right back at '0' as the best performing spot.
I've also seen where people found a shaft collar at the hardware store that was a slip fit over their barrel, and used that to tune with. IIRC they used the tail of a pair of calipers to measure the distance from the muzzle, and secured it with set screws. Other people have used hi-temp O-rings stacked on the barrel a few inches back - add them two at a time til the groups start getting smaller, then when they start getting bigger, remove them one at a time. It doesn't take much. If you're intrigued by the concept and want to test the waters without having your gun permanently modified, it might be an option worth trying.