How has federal mandates been used to increase the power of the federal government relative to the states?

After the Civil War, nobody in power dared to raise the idea that states could nullify Federal Laws or secede from the federal union. Various supreme court decisions and rulings by federal judges have pretty well brought state constitutions and state laws into to line with federal law.

Furthermore, Amendments to the US Constitution such as the 13th, 14th, 15th, 16th, 18th, 24th, and 26th Amendents increased the scope of the US government, while the 17th Amendment drastically diminished the powers of the State governments and increased the freedom of action of the US government.

And further yet again, the large Federal revenues resulting from the 16th Amendment and Revenue Act of 1913 have enabled the US government to control the state government using tied and conditional grants, for example in withholding federal road funds from States that did not enact the federal speed limit in 1973 (abolished in 1995), or withholding federal education grants from states that did not adopt the provisions of the No Child Left Behind Act in 2001.