That's odd mine does,
The only way I think that can happen is if you have multiple windows as it seems to use the last opened size, or if your closing the window using the red x instead of just quiting will reset it.
Back in the day, I used OmniWeb exclusively in MacOS X as it was one of the few browsers optimized for the OS. Eventually, I switched to Camino (anyone?) when OmniGroup slowed development.
Maybe I'll load it up for the memories...
I have just tried your suggestion, and it does not work. On next launch, it reverts to default size, which is way too narrow for comfort.
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I did the reverse, because Camino fell way behind on today's needed filtering features.
That is odd, just tried (firstly I dragged the window to make my preferred size) then I right (second) clicked the Roccat icon in my dock and chose quit. I then relaunched and it used my new size - I even tried having multiple windows and they all restored to the size I set them too. So not sure why it's not working for you, what OSX cat are you using?
Hmmm I tried it on a Snow Leopard iMac at my work place and you're right.
It works perfectly in Mountain Lion and Lion though.
Really strange..
On the idea of browser with page previews in the tabs, Opera does this in the way I've found myself to be the most comfortable. Opera retains traditional tabs, but when you roll your mouse over the tab, a preview of the webpage is displayed.