I can't address your questions about RapidWeaver or Stacks, since we don't provide those, but I can at least say that our box.js cart overlay script should automatically detect when the buyer is on a mobile device. In that case, the cart buttons work in "fallback" mode, opening a separate window/tab to display the cart. This makes best use of the available screen space on mobile devices vs. displaying the overlay-style cart inside your page.
I've submitted some proposals to Development to improve the fallback cart's responsive design; meanwhile, until they have a chance to implement those, you can help matters by making sure any custom logo/header image you may upload to us is no wider than 320px, as the width of that image currently determines the minimum width of the fallback cart's layout.