Origin of 'cuz' as shortening for cousin?
According to Green’s Dictionary of Slang the abbreviation dates back to the 16th C. so probably a BrE expression originally. Note also the Black AmE usages from the ‘60s meaning friend or as a generic term of address among males.
cuz n.:
also coz, cuzz, cuzzy;
[abbr. SE cousin, a development of mid-16C–mid-19C coz]