I'm currently working on a system which has a fullscreen map and uses dialogue windows floating above this to house content and forms.
When designing the system I had always planned to allow resizing and had started my mockups working this way, however, after some thought I removed this.
In my case I was having to make very specific layouts for each popup. The content has next to no repetition. After designing each one for the best UX I then had to re-work it and make it re-sizable. This was moving fields around and meant that any sort of user familiarity with field positions was lost due to the user's own actions.
I think the question you should ask yourself is; will the system within the window provide better or worse UX if it's resizable?
In my case the answer is worst so each dialogue is given a size which fits the content in most naturally and it stays that way. Users expect the windows to be resizable if they're used to windows OS as that encourages full screen, whereas I found mac users don't expect it as much as they're more used to having tiled windows.
Can you give us a hint towards the type of user this is aimed at? Is it trained staff or public? Also, how small are these popups?