I built Midori browser, but it would probably need a lot of hacking to make it work. Initial state is that the main window opens, but menus don't work and it is unstable.
I had more luck with SkipStone
. This one works quite well after minor adjustments. If I find time I will work more on it.
Or maybe there are some other lightweight browsers that use webkitgtk?
Edit: You will find more info in this thread.