I know this is an old post, but unanswered questions bug me, so here goes. All you forum searchers can thank me later.
So, it turns out that there is a very simple fix for the "Statsfile not found" error, and it is in how you are converting the file. When opting for 2-pass conversion (which is recommended for best results with *.avi files using the XviD codec), the first pass must be completed before the 2nd pass can be started. For whatever reason, when selecting the XviD codec, 2nd pass 2-pass conversion is selected by default, which requires the statsfile created from the 1st pass to operate. Within Encoder Options, there is a second button for changing codec settings. Click on this and change 2-Pass 2nd Pass to either 2-Pass 1st Pass or Single Pass. This will eliminate the error and allow your conversion to execute.
As far as your filesize issues go, I've got nothing.
Good Luck!