I would usually expect to see this kind of behaviour with a "property : value" construct, where properties would usually be stored back into the script.
After running your script a few times, it seemed to me the file size stopped increasing after a certain point.
I can't really comment on why exactly this is happening, I've not experienced such a thing before. I never had to use active script or display info about it.
Could you give us some background on what exactly you are using it for? It seems unusual to have to display the current script name or location. Maybe there is a better way.
Have you tried simply setting the var to nothing at the beginning of the script? It's not necessarily elegant but it might do the job.
OSX 10.6.8, IDCS5, Script Debugger 4.5x
That's normal behavior. When an app runs a script, it then saves it back to disk. That version contains the contents of any modified properties, as SuperMacGuy says, but it also includes the value of any *top level* variables. So you need move any variables you don't want stored out of the top level of the script -- essentially put it all in a handler.