Is there a powerful yet lightweight vim-like keyboard-centric web browser out there (for Linux)?

Here are some to try:

• jumanji.
• Vimprobable
• dwb
• luakit

There's uzbl. It follows well the UNIX philosophy, and it's very slim. If you're looking for lightweight and extremely functional, this is it.

Conkeror is probably the most keyboard-oriented graphical browser I have seen. Apparently it even supports some Firefox extensions. I've never used it myself as it takes a while to learn the keybindings, but maybe you will like it.

Have you tried Opera yet? When you install it go into the settings and enable UNIX Keyboard shortcuts. Things like ^U work, you can tab through links on the page and select them. They even have a page dedicated to how to use the browser without a mouse:

http://www.opera.com/help/tutorials/nomouse/