OmniWeb does what you want, ERICBRIAN2002.
First of all, hide your Dock. OmniWeb, because it intelligently knows when the Dock is active, doesn't allow you to resize behind the Dock, which is good, because then your resize widget doesn't get obscured.
Now stretch your window from corner to corner (you still won't be able to do it all the way because OmniWeb wants to make sure that you don't unhide your Dock when you're reaching for the resize widget, which is also a very nice feature -- I don't think 2 rows of pixels matters that much). Then choose "Save Window Size" from the "Browser" menu. Now whenever you create a new window it will be saved with that size. Note, however, that if your Dock is unhidden, it will make the size smaller so that the resize widget will never be obscured. However, if your Dock is hidden, the size you set will be preserved.