Weebly is this webservice
Comparing HTML & weebly is like comparing cooking and going to the drive-in of some fastfood.
Weebly is a key in hand service from what I understood, whereas with HTML (as base) you have to build and host your website all the way.
If hosting is something you're already familiar with, you might want to take a look around at some CMS (joomla, drupal, elgg, ...) that might allow you to host/distribute your games (they are just some HTML/JS code addition in a page/article) and already has some membership system in PHP.
If you have no clue about all this, maybe go with the webservice if they offer good companionship on the configuration/maintenance. That'd probably be the simplest.