Are you putting the SWF on BB or do you upload a package that contains not only the SWF but also the companion JS and HTML-files?
In the last case, you can change the HTML-file and replace the fixed width/height by 100%. Beware: resizing to another size than the original always results in quality loss.
I upload all three files. Here is what the first frame of the video normally looks like, for reference:
Based on what you said, I opened the HTML file in Notepad and changed...
var so = new SWFObject("Unit 2.swf", "Captivate", "1281", "985", "10", "#CCCCCC");
var so = new SWFObject("Unit 2.swf", "Captivate", "100%", "100%", "10", "#CCCCCC");
When I did that, the first slide looked like this:
...and changing the size of the window doesn't affect the size of the video. Any idea why this is happening?