Lightest, cheapest laptop out there with best battery life

My laptop is showing sings of death, and I know I will need a new one soon. Also, I am planning to get a tablet and ditch my smartphone, and to stop using the laptop for browsing content: I'll do most of that to the phone/tablet, and use the laptop as an authoring tool: writing and coding.

So I am looking for a laptop that is cheap, light, and can keep running for at least 3-5hrs under mild Debian+Emacs load. Ideally around 11"-13".