What makes you think it is not heard in Britain as well? It is an increasingly common colloquialism, chiefly because no-one corrects children when they misuse language so incorrect usages become accepted usages.
I don't think it's a question of emphasis: I think it's commonly used by analogy with "out of", as in: "Get out of my pub."
There's no particular reason why we should say "out of" but not "off of" except that in standard English "off of" is considered incorrect. You might make the point that the "of" is superfluous, and that is true; however, it's also superfluous in "out of", but "Get out my pub" is also non-standard.