Browsers that support the Resource Timing v2 has the ability to get the size of every resource response (not for the main page, there we need the Navigation Timing v2) so we can calculate the total size. Firefox 45 supports RT v2 and Chrome has it in it's timeline.

The Performance inspector can then show the total size, image sizes and warn for large assets (=images larger than X kb).

Lets use the Resource Timing V2 where it's available, for other browsers we do a request extra for each URL and check the headers for the right size.