One solution is to use Apache virtual hosts. For the AF pre-provided info on Apache virtual hosts, see XAMPP Dashboard | HOW-TO Guides | Configure Virtual Hosts.
Using root relative paths means you only have to provide the path (with leading slash) after the root of the web server. For XAMPP, the root of the Apache web server is C:/xampp/htdocs/. However, in your local, the root your web site(s) are C:/xampp/htdocs/www/Websites/NameOfWebsite/, which is not the root of the XAMPP Apache web server, which is why your root relative paths are not working locally.
In short, to use Apache virtual hosts as solution, in the Apache httpd-vhosts.conf file, copy one of the <VirtualHost *:80></VirtualHost> sections, make sure it is not commented out, and (in your case) set DocumentRoot to "C:/xampp/htdocs/www/Websites/NameOfWebsite/", which indicates the path to use as root relative path. Then set ServerName to
http://www.websitedomain.com, which indicates the domain name to "register" to the DocumentRoot. Lastly, in the Windows\System32\drivers\etc\hosts file, add line 127.0.0.1
http://www.websitedomain.com and make sure it is not commented out. This DNSs/resolves the domain name entered into the web browser to 127.0.0.1/localhost. If necessary, restart XAMPP Apache to use new httpd-vhosts.conf, and restart web browser to use new hosts file.
Play around with virtual hosts. It works. Moreover, it scales to use one XAMPP installation to support the development of multiple web sites locally as follows. In the Apache httpd-vhosts.conf file, register each root relative path to its domain name (all uncommented out). In the Windows hosts file, DNS/resolve each domain name to 127.0.0.1/localhost, all commented out except the one that you want to use currently/presently locally. Please re-read that last line. Again, if necessary, restart XAMPP Apache to use new httpd-vhosts.conf, and restart web browser to use new hosts file.
Hope it helps.
Steve