Dude, you are in serious need of a history lesson. First, the 14th Amendment overturned Dred Scott, not the 13th. But this was still a country based on segregation, lawful discrimination etc. Ever heard of Plessy v. Ferguson (1896) and "separate but equal"?
In case you missed it, what ended segregation in this country was Brown v. Board of Education (1964). Another SCOTUS case, mind you, not a legislative act or amendment. Congress got it's act together the same year with the Civil Rights Act, and the following year with the Voting Rights Act, but it was the Supreme Court that had to step in and end segregation.
Regarding the 10th Amendment, its erosion started long before the current court and the Obergefell decision. Griswold v. Connecticut found a right to privacy in the "substantive" component of the due process clause of the 14th Amendment. The right to privacy is not an enumerated right in the Constitution, but is nonetheless a right granted federal constitutional protection.
Griswold is one of the most significant cases of the 20th century with respect to it's broad interpretation of the due process clause. If you really want to understand the courts ruling in Obergefell and how it relates to the 10th Amendment, you should start there, and then follow the evolution of this legal concept (and Scalia's highly entertaining opposition to it) in the cases that followed...Roe v. Wade (and it's progeny cases...Casey, Carhart...), Lawrence v. Texas, Loving v. Virginia etc.