The 19th century term “white mans burden” reflects the idea that

it is the boston port act

it is a part of john locke's natural rights popular during the age of enlightenment that people had inalienable rights to life, liberty and property. this was reflected by thomas jefferson in his declaration of independence as rights to life,liberty and the pursuit of happiness.

another line in the declaration of independence is that people have certain rights just because they are human. humans are capable of obeying the three natural rights john locke mentioned making them governable by these laws and therefore entitled to these rights as well.