I am trying to posit a simple way to use pure Special Relativity (SR) to approach relativistic mass. And from there, I think we might be able to make some conclusions about whether so-called "relativistic mass" gravitates or not. We start with a simple laboratory (lab) reference frame, and let it be inertial for now. We put a treadmill device at rest on the floor of the lab, and then turn on the treadmill so that the belt is moving horizontally at constant speed, parallel with the floor of the lab. Let the bed of the treadmill be arbitrarily long, like a long conveyor belt, so that we can treat an arbitrarily short segment of the belt as an inertial frame. We will call the inertial frame of this segment the belt the "belt" reference frame. At this point there is no acceleration in the scenario, and since this is pure SR, there is no gravity. So, a spring scale with a mass on top of it would have no reading, because the mass would be essentially "weightless" on the scale. This would be the case regardless of whether the scale & mass are at rest on the floor of the lab, or whether they are at rest on the belt. In both cases the scale reads the same, in this case a zero value. Now we let the whole lab frame accelerate upward at a constant rate. The floor of the lab and the belt now both have an acceleration similar to gravity, and the spring scale now displays a reading for the weight of the mass. There is still no difference whether the scale & mass are at rest on the floor of the lab, or whether they are at rest on the belt. In both cases the scale reads the same value, in this case a non-zero value. Thus we conclude that any so-called relativistic mass added to the mass due to it moving through the lab frame on the belt, does not contribute to its gravity, as measured by the weight of the mass. Is that conclusion warranted, or am I missing something?