I wrote HTTP::Size to do just this. From the docs:

get_sizes( URL, BASE_URL )

The get_sizes function is like get_size, although for HTML pages it also fetches all of the images then sums the sizes of the original page and image sizes. It returns a total download size. In list context it returns the total download size and a hash reference whose keys are the URLs of the images found in the HTML and whose values are hash references with these keys: