Wanted to pass this on in case any others are having trouble with it recently:

My site's main page had looked fine on iOS phones for months, ever since I first built it back in June. But in recent weeks, my main page started rendering with a black right border as if there was some kind of non-responsive content or setting on the page.  All my other pages were fine.  I went through chat support (#3831500 for the weeblies) and that gave me a good lead to follow with regard to embedded code on my page, but ultimately that wasn't it.  What I ended up doing was copying the main page to a scratch page, and removing content piece by piece until the border went away, and also using Firefox developer tools to look at the weebly generated content. I found that where I have page elements organized in columns, if the Spacing value between columns was > 30, I would get the unwanted border.  If I kept it under 30, the border went away. 

Now, I don't know what's magic about "30", whether it's relative to something else on my page, or something new in how weebly is spinning the code, because the same settings on my page rendered fine before.  In the Firefx code Inspector I see padding values of 30 applied to the column table definitions...which is what gave me the above idea.

Long story short: if you're having trouble with borders around your pages on devices, you may want to tweak your column spacing values as something to try first...might save you some time.

Ryan