There is only one version of HTML5 to cook and package. However, there are 32-bit browsers, as well as 64-bit browsers. Depending on the browser you’re using, the game may not work. Google Chromium 64-bit should work, as should 64-bit FireFox Nightly. 32-bit browser for FireFox should be working as well, but not Google Chrome 32-bit at this time.
I created a test weebly account and I do not see a way to actually upload an HTML5 project to this site. You may be able to find a way, but it looks like it only uses specific files, HTML5 doesn’t look like one of the supported file formats. But if you want to create a website, you simply just add the HTML5 packaged project folder into your website and you should be able to set it up from there.
If you have any further questions, feel free to post back here or submit a question to AnswerHub.