Backup Exec 2010 and Exchange 2010 data grwoth

My company migrate to exchange 2010 for sometime, but we found that the exchange data keep growing

E.g. One of the DB around is around 290 GB now, has been growing in 5GB per month for 1+ year.

I can see the mail DB has record full back lately, the log is purge.

When I dig into the mail DB, I can see some mailbox is having huge "TotalDeletedItemSize"; say mailbox is less than 100MB have 1G TotalDeletedItemSize.

Is there anything about to do with backup exec so the exchange did not clean up these hug items.

Thank you