The lighter the bullet, the more velocity will fall off at longer ranges, but stability will not change with range if the bullet fits your gun properly and the gun is set up the way I recommend them to be.
When I developed the LBT styles I tested all the revolver bullets at 350 yards to be sure they would be stable at any range. When I make a recommendation, you can count on the bullets to be acurate for the use and velocity range you have asked about.
When ever I devlope loads for a revolver I always do the first testing at ranges of at least 100 yards, and prefer 250 yards or more. An arched trajectory can be expected of coarse, especially with low starting velocities, but if ALL the bullets don't drop into the same spot like a lazer I consider the load no good. This isn't a target chasing endeavor, but just aiming at a relitively small rock on a mountain and watching POI. If they all land in a a 12 inch area or less, that load will punch a ragged hole at 25 yards, and the load is proven with the first cylinderfull. I do this whether the load is starting at 800 fps or full magnum loads. The same precision is mandatory.
With heavier weight bullets, like 300 gr plus in 44 magnum, relitively high velocity up to maximum loads is sometimes required to get them stable, depending on twist rate of the gun of interest. Lighter bullets stabalize at far lower speeds.
One cannot be sure on long range stability by shooting groups at 25 yards, as instability isn't always showing enough to be visable at that range. A tiny wobble which one has to use a magnifier to see in the bullet holes, though they are printing a nice group, can go crazy out at longer ranges, often flying so wild and scattered that it's hard to spot impact on the side of a mountain.