It's actually the imperative form of なさる, an honorific version of "to do". When paired with the conjugative stem of a verb it expresses extra politeness. Also commonly seen in (e.g.) "good night/sleep well": おやすみなさい
Yes, I've lived in the USA my whole life and "Big Brother" is what you call your room mate who goes through everyone's mail to insult him for spying. "Older brother" is what you call your male sibling born before you.