I think that the stiffer the barrel, the more weight is required. Dan Lilja has a free program that can be downloaded from his web site that can be used to calculate barrel stiffness.
The fellow that has had the greatest success (in short range CF group shooting) with tuners is Gene Buckys. He takes an entirely different approach as to how to use a tuner. Based on his experience, he believes that you can get into trouble moving a tuner during a match because if the adjustment threads do not seat perfectly, accuracy can be adversely affected. He has seen this happen. He has also said that he has never had a barrel that shot more accurately because of a tuner, but that the breadth of tuning nodes is increased, making it easier to stay in tune. What he does, is to thread a new barre for a tuner, tune the load for peak accuracy, install the tuner, and adjust it by shooting, and then lock it down, never to be moved again. From there on, he tunes conventionally with his loads. Others that I know have been beguiled by their experiences playing with adjustments, but in the actual heat of battle, where time is short, and pressure high, making a mid match adjustment has not been as successful as when in a more leisurely practice session. One thing that needs to be said is that Gene is a group shooter, and in that game, there are few successful shooters that preload. On the other hand, running something like a .30 BR for score shooting, may be quite a bit different. What will get it done for one, well may not for another.
I have several tuners, and have played with them some, and shot one weekend with one at a group match. Based on that experience, with a 6PPC sporter (10.5#), I am inclined to Mr Buckys' approach for future tuner work.
For rifles that are of the same weight as mine, if they are to be shot free recoil, the issue of balance becomes very important. (If the rifle is shot with some other style, that is less of a consideration.) In order to keep a rifle balanced for free recoil shooting, I think that it is best to not have too heavy of a barrel profile. When I set up my rifle for the first tuner that I tried, I was already at the weight limit, so we took off the same amount from the barrel as the tuner weighs. This barrel had been middle of the pack at best, throughout its life, and after installing the tuner, shot quite a bit better than it had, even though it had a lot of rounds on it at that point. For this reason, I think that tuners probably hold some hope for one barrel at a time shooters. While they may not improve the absolute accuracy of the finest barrels, I believe that they can for more average barrels. This is not only based on my experience, but that of a shooter who actually had this happen with several barrels that had not been competitive.
As a final thought, I would recommend that anyone who wants to learn more about tuner theory works study Varmint Al's web site, reading and rereading that material as many times as it may take to fully understand all of the subtitles that it contains. He has made a tremendous contribution to my understanding of what can be a difficult subject.
I enjoy reading of others' experiments, and always try to keep an open mind.