Windows remembers the last screen size but not if you use the maximize icon at top right.
Open a webpage. Stretch it out to fullsize by using your mouse to drag the top, right, bottom, and left borders; don't use the maximize button!
Now choose any link on that webpage and right-click> open in a new window. Stretch that second window out to the desired size as you did the first window earlier - and don't use maximize.
Close the first IE window with File, Exit. (Do not use the "X" icon at top right unless you hold down the Ctrl key while doing so.) Then close that resized window by either File, Exit or Ctrl+the "X" icon.