There are two things going on here.
Rendering to a new track is not particularly helpful. You just want to render the selection to a file.
The other thing is that the size of the resultant file will depend entirely on what format you are rendieing in.
For example, if your imported 15MB file is low resolution wmv but your render it as uncompressed AVI, the file will be much, much, much, bigger (note it will not be better quality just much higher resolution low quality)
So, you need to do the following:
1. Establish the codecs, file type, resolution etc of your source.
2. Set your project settings to match
3. Make your selection on the timeline
4. Render - and set all your render settings to match the source. (and make sure the "render selection only" bock is ticked.

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Tim