kennym: String stability to me is not elongating on the bow. Dacron, even when it's shot in, tends to elongate under warmer temperatures. It also has more stretch at the shot compared to the low-stretch strings.
All strings have some stretch, though the newer low-stretch strings have very little. Made extremely light i.e., low strand) they might stretch a bit at the shot, but again, not as much as dacron, and not enough for most people to notice, and they still reduce limb vibration and hand shock more than dacron. Made standard or heavyweight, there's virtually no stretch, at least none the archer could feel. And, the low stretch materials aren't as susceptible to temperature fluctuation as is dacron. In short, they're more stable.
A skinny string shouldn't be any harder on the fingers than a normally built string because it should be served to the same thickness (as previously used strings) to fit the arrows one already uses.