A really big database size I'm dumping the database every 2 days, but I noticed that at some point last month the database jumped from around 500 MB to 4 GB! 

What can be the cause of it?
One reasons that a database can grow w/o bound is when you don't have cron setup to run.  Check your "Recent Log messages" at /admin/reports/dblog  and filter for cron, and make sure it is running (nightly is a good start).

On of the things cron does is prune the cache, watchdog, and sessions tables.  These can fill up quickly with data that isn't critical to Drupal running.

Occasionally, clearing these out can take too long for a cron run.  If this is the case, running a manual query, such as

DELETE FROM watchdog;


may be needed.  As mentioned above, you can run this on the cache and tables beginning with cache_, watchdog, and sessions.  It is always best to take a backup first, before running DELETE queries.