You are converting the avi file to dvd-video format. The mpeg2 codec used in dvd-video is inherently less efficient at compression than many modern codecs found in avi files, like xvid or divx. The jump in size is therefore normal
It is often times easier to simply get a dvd player that can handle avi files without conversion. They aren't very expensive these days. You can then burn the avi files to a disk as data, and not have the increase in size.
Xvid and Divx are the most compatible video codecs for these dvd-players that can play avi files. If you don't know what is in your avi files, examine them with MediaInfo or Gspot video utility.