Looking at it now, it seems to not be directly related to transparency, but perhaps the export settings in FW. So it may have to do with the GIF format or compression settings. I didn't notice it when I changed mine... or to say I didn't look at the file size until AFTER I changed it to no transparency... so I missed that. Here is a comparison, transparency setting is on the bottom left of each image, file size is the top right.
So you can see there is basically little difference in the transparency setting... it must be somewhere else.