Roe vs Wade was a case in the Supreme Court - a legal precedent but not statute, as the Abortion Act 1967 is in the UK. It was won on the basis of right to privacy that a woman had a right, in consultation with her doctor, to have an abortion. But, because of the federal system of laws, it means that responsibility for regulating abortion is devolved to individual states.
For example, some set such stringent requirements for licensing of clinics that it's virtually impossible for any medical facility to comply. They can't say they are banning abortion. Just saying only centres meeting licensing requirements can provide them.
As for a 6 week limit, diagnosis by ultrasound is probably what they would use.