The Constitution is an agreement between the states, not individuals. When ratifying the Constitution the people of a state voted to join the union as the unit of a state not as individuals. That makes the states the constituents not the people.
If that was all there is to it, there would have been no House of Representatives. But people who authored the Constitution knew full well that it was not just about the states:
"... if, in a word, the Union be essential to the happiness of the people of America, is it not preposterous, to urge as an objection to a government, without which the objects of the Union cannot be attained, that such a government may derogate from the importance of the governments of the individual States? Was, then, the American Revolution effected, was the American Confederacy formed, was the precious blood of thousands spilt, and the hard-earned substance of millions lavished, not that the people of America should enjoy peace, liberty, and safety, but that the government of the individual States, that particular municipal establishments, might enjoy a certain extent of power, and be arrayed with certain dignities and attributes of sovereignty? We have heard of the impious doctrine in the Old World, that the people were made for kings, not kings for the people. Is the same doctrine to be revived in the New, in another shape that the solid happiness of the people is to be sacrificed to the views of political institutions of a different form?"
It is too early for politicians to presume on our forgetting that the public good, the real welfare of the great body of the people, is the supreme object to be pursued; and that no form of government whatever has any other value than as it may be fitted for the attainment of this object. Were the plan of the convention adverse to the public happiness, my voice would be, Reject the plan. Were the Union itself inconsistent with the public happiness, it would be, Abolish the Union. In like manner, as far as the sovereignty of the States cannot be reconciled to the happiness of the people, the voice of every good citizen must be, Let the former be sacrificed to the latter."
And here's a bit more specifically on the nature of the government that they were trying to establish:
"The proposed Constitution, therefore, is, in strictness, neither a national nor a federal Constitution, but a composition of both. In its foundation it is federal, not national; in the sources from which the ordinary powers of the government are drawn, it is partly federal and partly national; in the operation of these powers, it is national, not federal; in the extent of them, again, it is federal, not national; and, finally, in the authoritative mode of introducing amendments, it is neither wholly federal nor wholly national."
