Weak Cosmopolitanism and Immigration

Ran across the term "weak cosmopolitanism" in a newspaper piece today (don't remember which paper or whether it was op-ed or book review).  Apparently it's  a standard term in philosophy--just try Googling it: "strong cosmopolitanism" is much the same to my eye as Christianity or libertarianism: the brotherhood of man, meaning everyone is equal in the eyes of God and other distinctions are meaningless and should be ignored; the "weak" version says that humans favor their kin, their neighbors, their tribe, their nation and there's no way that such distinctions can be ignored.

The strong version would eliminate all immigration controls; the weak version permits controls but requires universalistic criteria for admission.