I didn’t like any of the existing frameworks out there, so I just created my own framework.
Cascade Framework ( http://cascade-framework.com/ ) combines a very light footprint with feature richness bacause of an ultra-modular OOCSS based architecture. If you only need its core features, you need no more than 2.5Kb of framework code (minified + gzipped).
If Cascade Framework still isn’t lightweight enough for you, there’s now also a light version with 2kb in total. You can check it out at http://jslegers.github.io/cascadeframeworklight/ .
Also, consider that both Cascade Framework and Cascade Framework Light provide out-of-the-box support for responsive design for all browsers that support it, while serving a fully functional desktop version to IE6-8.
I use Cascade Framework as a boilerplate for all my projects.