The last few days have my exchange transaction logs grow by nearly 1GB an hour, but when I stop all the blackberry services the transaction logs only grow by 100MB an hour
What is the Blackberry Enterprise Server doing that is causing my log files to grow

... accepting mail that your blackberry users send?

Have you added anything to your infrastructure that sends out large attachments? Monitoring System? Archiving System?

BES doesn't do anything with your Exchange transaction logs ... treat it as an Outlook client.