I've heard good things about dragula[0]. It's 9.8kb minified[1], no dependencies and browser support goes all the way back to IE7. There are also bridges for all the major frameworks.
There are also a couple more transitive dependencies.
But the 9.8kB figure does include all the dependencies.
I actively hate spending bytes supporting IE (and especially such ancient versions as IE7), and if necessary maintain forks of any libraries I use to avoid doing so; so I tried ripping out IE support along with crossvent and a few obsolete and/or bad abstractions, and quickly got it down to 7kB minified, and I expect one so inclined could shrink it further. (The crossvent part can be done in two minutes, it’s that simple.)
I should really make a feature of this kind of thing on my blog, I enjoy doing it so much.
I wouldn't say "all" the major frameworks, though (just Angular[JS] and React).