I ran through the installation process as outlined in the README.
First, a fresh installation of weewx...
I used apache2 (you said it also failed using apache), the latest weewx pip installation, and an updated debian based raspberry pi 5.
Copied the supplied weewx-data/util/apache/weewx.conf over to the /etc/apache2/conf-available/ directory, changed the 2 paths within that file to reflect the changed home directory, enabled the conf and restarted apache2. After the permission problem noted by vince that gave me a working weewx (simulator) , it displayed the html data / images. That permission change was to the users home directory, and it was set to 0755 - the weewx-venv install of weewx set the correct permissions for the main weewx-data directories.
CAVEAT: That's done with the weewx default installation of public_html being located in the users home directory. We could have a long, possibly animated discussion about the merits of that but for these purposes I'm going with the default installation of HTML_ROOT. ( If user www-data is added to the users group then 0710 is sufficient. YMMV.)
With that done, I installed wxobs as per the README, noting points 6. and 4. as required (that's the modules and test.php script) and restarted the webserver.
That resulted in the usual failure (red text) on viewing the wxobs/index.php page from the browser. By then following the procedure outlined there, ie:- creating /usr/share/php and cp -p the wxobs_weewx.inc file to that location it was ready for a retest. (those points are also noted in the README). Reloaded the browser and - viola - the page displays the database contents for the current date, and the calendar works to change it..