Obviously, I want to get the answer without saving the page. It seems basic, but I can't figure out how to do that. If it requires a plugin, it's ok. It would be nice if the solution would also cover styling sheets, scripts and images, associated with the page.
Open Developer tools (Ctrl+Shift+I or Settings Icon at the top-right of your browser window =>
In the Size column you'll see the size of everything loaded (Documents, Stylesheets, Images, Scripts, ...). You can enable filter to help you find out only needed stuff at the bottom-center of Developer tools frame.