www.wysiwygwebbuilder.com

I am looking to add some simple forum to the site. No need for any fancy features (groups, categories, Emailing etc.) , just something simple forum. I know phpBB, bit it might be overkill, and I want something I can integrate with WWB site (possibly free or cheap).

Any recommendations ?

There is no forum extension as such. A forum generally runs separately from your site as a standalone.
Maybe the following from php jabbers may be of interest.
https://www.phpjabbers.com/php-forum-script/
or one of the following so cheap it is "free"
https://mybb.com/
https://www.simplemachines.org/
https://mylittleforum.net/index.php