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.