Welcome to the forums!
Unfortunately, we are going to need a little more information. First, you have to realise that there are over 800 different types of Video formats that use the .AVI extension. It is just a carrier or wrapper format. And the files go from Raw AVI which is huge (65 GB per hour of video), through DV/AVI (still large at 13 GB an hour); through to the other end which are highly compressed mpeg-4 type formats such as DivX or XVid which will only take up 700 MB or less per hour of video.
Now I suspect you have one of those formats, but I can only guess as I cannot see your computer...

So please right click on your .AVI file within Video Studio -- either in the timeline or in the library window, and copy ALL its Properties here please.
Now you say you are using mpeg-2 as the rendering format. Well, if indeed you have DivX/XVid video to start with, that is mpeg-4 which is much more compressed than mpeg-2. So it is natural that if you are rendering from mpeg-4 to mpeg-2, the final size will greatly increase. I am afraid there is no mystery in that -- it is simply the nature of the beast!
If you want to produce a video in the same format as your original file, then clearly you would not be choosing mpeg-2 for the rendering. You would be choosing either (1) Share > Create Video File > AVI, and then making sure you are choosing the same codec for the rendering as your original video; OR (2) if your .AVI is in the timeline first, then choose Share > Create Video File > Same as first video.
But you also don't tell us what you are planning to do with your rendered video. If you intend to burn a video DVD, then rendering it to mpeg-2 as you are doing is the correct format for a video DVD. But that means you have to accept the significant increase in file size that goes with this conversion.
.AVI is not a format which can produce a video DVD. However, if it is indeed a DivX file, and your stand-alone DVD player is rated to play DivX, then you can burn a DivX file in its original format to a CD or DVD but as an archive file, not a video file. You can't do that in Video Studio. But with such a data CD or DVD with Divx on it, then if you put it in a DivX rated player, it will play much the same as a video DVD.