Your best bet would be to upgrade your store to the latest Zen Cart and upgrade your PHP at the same time. You're running very old, hackable versions of both.

Log files don't generate database entries, so that's not the cause of your database size increase. To determine where the growth is in your database, use phpMyAdmin and sort on table size (it's a column at the far right). If I had to take a wild guess, I'd say the email archive table because your store has been converted to a spam server, but that's just a guess.