Not exactly clear on your "pop-up window appears". If you tell me what web-site it is you are accessing maybe that would be more helpful for a couple of reasons.
I am not sure if the box is a:
(1) resizable java type pop-up window you are talking about.
(2) A new page.
If it is option1 then the page will always return to display in it's default size when you close it. (The size you consider to be too small)
Unfortuntely there is nothing which could be done about this. Purely a fact that the web site designer created too small a box for your liking.
However, if it is a problem which has recently occurred then one way possibly to fix it would be to do the following.
Open Internet Explorer.
Click Tools > Internet Options > Advanced.
In the bottom right-hand of this window click the restore defaults button.
Then access the web-page and see if this helps.
HTH