I recently bought a cheap&small office laptop with intention of taking it with me and completing assignments in public places. Problem is, it chokes up and dies when running more than eight tabs on firefox. I also tried k-meleon, it has great performance but the UI is ancient and many websites that I need dont support it.
NOTE: I use Linux, so some (or all) of the light-weight web browsers I use, might be unavailable if you use Microsoft Windows.
The web browsers I’d recommend are; NetSurf, Dillo, and w3m (text-based). Unfortunately I can no longer recommend Midori due to a change in leadership / implementation.