Give SFTP user rights to /var/www/html

If you make /var/www writeable by its group and add the user to the group, that user will not have to use sudo. Try this:

sudo adduser  www-data
sudo chown -R www-data:www-data /var/www
sudo chmod -R g+rwX /var/www

The user should then be able to edit /var/www/ files without hassle.

The first line adds the user to the www-data group, the second line clears up any files with messed up ownership, and the third makes it so that all users who are members of the www-data group can read and write all files in /var/www.

If you are logged in as you need to log out and log back in for the group membership to take effect.