I have been having trouble with my MBP since I got back from vacation. I could not tell what it was initially, just sluggish — but not super high disk IO or CPU. I did not think much of it until the last two nights when I was at home my internet was really slow too from every device in the house. I tracked the usage down to the Mac consuming all available outbound bandwidth. Activity monitor reported the same high (> 1 megabit/second) usage. So then I pulled up WireShark to see what was going on. All the packets were for destined for my company's ActiveSync server. Sure enough, I shut down Outlook and the problem disappeared. No high bandwidth, no sluggish response. Start Outlook back up, bam - issues returned.
Outlook was not showing any active sync tasks so I just started cleaning up -- first my Inbox, also cleaned out the Deleted Items, Drafts, to no effect. Then, I cleaned out my Sent Items and poof, the high bandwidth disappeared. Googling shows this is a rare, but typical issue. Upon the failure to Send a "large" email, Outlook can become confused and continue attempting to send the item even though you have cancelled the email.
Instead of following the typical online recommendation of deleting the entire Identity (which includes ALL Email and Calendars items, backup/restore), you can simply right click on your Sent Items and Drafts, and choose Folder Properties, then click Empty (save what you want first). That does empty those folders, as well as force a clean resync from OWA.
So, if this happens to you, or you see ultra high network utilization on OWA, this may be the problem.
For me, it was a 20MB PDF I tried to email...