Join us January 15th for an AMA with Champion Achaia Walton, who will be talking about her article on Event-Based Reporting and Measuring Content Groups!
Unfortunately, that isn't something we can capture automatically at this time. Neither JavaScript nor HTTP headers have access to size across multiple assets. However, if your server can track file sizes that it is sending to the browser, you may be able to set a custom variable to capture size. That would allow you to do averages.