We need to study how httrack web copier works.
#1. Download that tool and try to access your site using it.
#2. While that tool access your site find what is the "User-Agent" value is being sent by that tool. Using PHP you can write code to find the user's "User-Agent"
#3. After finding it.. Block that particular User-Agent via php code in .htaccess or php code.
Completely change your site to work ONLY for registered & logged in users.
Once they signup an account and use that software to download all of your pages.. Then., Find that bad user and ban him. It is easy to find logged in user's browsing activities.