We've been focused on finishing up the new Admin as a prerequisite to implementing any new features or functionality, so we don't yet have a way to remove the sign-up checkbox from checkout pages we control (for Free Checkout and card-based direct payments).
Regarding the Aweber aspect in particular, they should soon start supporting our standard custom/third-party Integration feature, so once that's ready, Aweber integrations which use or upgrade to that method will disregard the sign-up checkbox, just as MailChimp, Drip, and GetResponse integrations already do.