Are you sure they aren't charging for bandwidth use, which is a measurement of the amount of megabytes of files that are transferred between the web server and the computers that are viewing the site.
As an example, if you have a page that is 5kb but it has a 1mb image on it, every time someone views the page they could use up just over 1mb of bandwidth, depending on whether it is a direct page request or whether they get a cached copy. If you have a high traffic site and 10,000 people request that same page in a day, you can use up a lot of bandwidth.
I've never seen a web host charge for the size of your site, although most do place a maximum site size limit of 10, 25, 50 or 100 megabytes or so. Most hosts are far more concerned with your bandwidth use than the physical size of the site.