I don't know much about moving the database - I've never tried that, although I believe that it expects the database to be wherever the Arcserve software is (Don't quote me on that, though)
Another approach: What is your database prune interval set to? It defaults to 30 days ie it will delete information from the database that is more than 30 days old. This means that your database will continue to grow for 30 days, but may well even out after that. (Please note, a prune does not make the database smaller, it effectively 'blanks out' old records within the database.)
My solution to this is initialise the database (using dbmgr.exe), and set the database prune interval to something smaller(14 or even 7 days). How small you set the prune interval to depends on how often you restore as, if the info has been pruned from the database you will need to merge the tape before restoring.
Also, check out the Arcserve\Temp directory if you are short of space. If you are having problems with your database you can get files building up in here, sometimes quite large. Delete these, but be ready to merge the tape if you have to do a restore.
Hope this helps.