Was the US Constitution a strong central government at the expense of states' rights?

Absolutely.

The framers of the Constitution, including Madison, Hamilton, and Washington, had watched the country deteriorate under the Articles of Confederation. The Articles had left the states fully sovereign, while the central government barely functioned (it could not even raise its own revenue. It depended on contributions from the states, much like the UN). They saw veterans riot over the Confederal Congerss' inability to pay pensions, and they saw Shay's Rebellion nearly cripple the government of Massachusetts.

The states also squabbled over their borders and fought for land in the west. It seemed that without a more unified central government, peace could not be guaranteed.

So, when the framers met in Philadelphia in 1787, they sought to create a government strong enough to enable free trade among the states, quell domestic rebellions, and stand strong on the international stage. To do this, they had to prohibit the states from acting independently. Thus, the new Constitution actually did, and was intended to, take away rights from the individual states, and create "a more perfect union." It was only the Anti-federalists (opposed to its ratification), who were in favor of retaining states' rights. From then on, the central government has grown stronger, and the nation has been more prosperous.