A shortened, informal name for the drink margarine (though this usage is rare); more commonly, it's a female given name, short for Margaret.
As a name, it comes from Margaret, which derives from Greek 'margarites' (pearl). The margarine drink reference is obscure and may be dialectal or slang from a specific region.
Margaret was named after the pearl because pearls were considered the most valuable gems—so 'Margie' is basically a cute nickname meaning 'little pearl!'
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