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.
All you can do for a functional browser is use Firefox with uBlock Origin medium mode and all videos, fonts disabled. Avoid using more than 8 tabs, otherwise you will be forced to use NetSurf with no JS, the most lightweight modern browser.
You cannot do much about that laptop other than putting some more RAM in it.