Microsoft Outlook for Mac - View Mailbox size
Sadly, Outlook:Mac 2011 doesn't make it possible for you to view your mailbox size at all times in the UI.  The method that you've found of viewing it via the Folder Properties is the only method.

If this is important to you, you should submit feedback to Microsoft.  In Outlook, go to Help -> Send Feedback About Outlook.  Tell them exactly what you want, why you want it, and how it impacts you to not have it.  Be verbose -- the better of a case that you can make, the higher the chance is that your feedback will be given due consideration.