How we cite our quotes: (Section.Paragraph)
Quote #1
An act for granting and applying certain stamp duties, and other duties, in the British colonies and plantations in America, towards further defraying the expences [sic] of defending, protecting, and securing the same; and for amending such parts of the several acts of parliament relating to the trade and revenues of the said colonies and plantations, as direct the manner of determining and recovering the penalties and forfeitures therein mentioned. (1.1)
The D-word is invoked here. They're talking specifically about the amounts of money that will have to be paid for the stamps, although it would also be the duty of the colonists to pay them. In the crown's defense, it also stipulates exactly what this money is to be used for, and in fact it's something that's already been done.
Quote #2
[…] we, your Majesty's most dutiful and loyal subjects, the commons of Great Britain in parliament assembled. (1.2)
Parliament characterizes itself as the king's most dutiful subjects. Clearly, the idea of adhering to duty was valuable enough that it was used as a bit of a brag.
Quote #3
For every skin or piece of vellum or parchment, or sheet or piece of paper, on which shall be ingrossed [sic], written or printed, any declaration, plea, replication, rejoinder, demurrer, or other pleading, or any copy thereof, in any court of law within the British colonies and plantations in America, a stamp duty of three pence. (1.3)
This is a standard example of what you'd find in the first part of the law. You're going to see "duty" once a paragraph there. It's talking about how much that specific thing will cost to have a stamped version. And once again, you can see how the two slightly different definitions of "duty" relate to one another.
Quote #4
And also a duty of one shilling for every twenty shillings, in any sum exceeding fifty pounds, which shall be given, paid, contracted, or agreed, for, with or in relation to any such clerk, or apprentice. (2.1)
This specifies a duty paid to an apprentice, which brings up an important point: duty as a concept goes both ways. People without power have duties to those who do, but people who have power also have duties to those who don't. This intersecting and interacting web of obligation is what we call society.
Quote #5
And be it further enacted by the authority aforesaid, That all books and pamphlets serving chiefly for the purpose of an almanack, by whatsoever name or names intituled [sic] or described, are and shall be charged with the duty imposed by this act on almanacks, but not with any of the duties charged by this act on pamphlets, or other printed papers; anything herein contained to the contrary notwithstanding. (5.1)
It's not enough to say that one has a duty to someone or something else. You have to specify what that duty is. This section of the law is one of several that clarifies what those are.