The way in which Windows decides what size a system dialog should be — for example, the one you see when saving or open files — can seem like sorcery. Fortunately, you do have some control over it and while not immediately apparent, it is straightforward.
As Addictive Tips Fatima Wahab explains, you can force Windows to remember the dialog size settings on a per-application basis. First off, fire up the program and get it to display the dialog in question, then, resize it to the desired dimensions. Wahab points out that the window must show at least one row of icons, otherwise it won't work.
Now — the important part. When you're happy with your exploits, hold down the Control key and close the window via its top-right "X". The settings will be saved and next time you open that particular dialog in the application, it'll return with its size intact.
It's a shame you can have this applied across the board — that would likely require an adventure into the Registry.
Set A Default Size For The Save As Window [Windows] [Addictive Tips]