The weaker notion of States' Rights as a metaphor for decentralized government is admirable. However, as with most "conservative" philosophies, the doctrine of State's Rights is sugar-coating on a hidden agenda. A person invoking it is usually rationalizing a less virtuous motive.
In this case, it is the fact that a bully can more easily bully and oppress a smaller group of people as opposed to a larger group of people, especially if there's nobody bigger (i.e. the federal government) to stop him/her.
"States' Rights" was invoked to justify slavery, secession, and later, segregation. The Ku Klux Klan actually ran Indiana in the 1920's.
Arguments for "States' Rights" are normally predicated on the 10th Amendment to the Constitution of the United States of America. This article states
The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
Of course, people arguing "States' Rights" frequently present it differently:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states,
a lie of omission. I really wish that my presentation of the above distortion of the Constitution were a straw man that I had set up to knock down; sadly, I've heard this distortion more times than I care to.
Empty sophistry, you say? The division of leftover rights between the states and the rights of people remains unclear? Not really. At the end of the Civil War, Congress passed (and the states ratified) the 14th Amendment:
No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.