When you have the 'Half-Size' window in front of you make it to the size you want before closing.
You can either do this by just clicking the 'maximize' button (usually the middle button top right of the window), or drag the window to the size you require by dragging the edges or corners of the window.
Once you have the window how you want it close it by:
File > Exit
DO NOT use the 'close' button ('X' top right hand corner) to exit...this will cause the window to open at your previous settings.
Once you've closed the window any further windows should open to the new size automatically.......you can then use 'X' to close the window again without losing your settings.
Regards.