The law on the books for Virginia for instance, did not speak at all too the Asian population, but ONLY to marriage between black and white.

That was actually appoint during the Supreme Court's hearing of Loving v. Virginia, where because the law only spoke about 2 races, it was clearly racially biased and thus violated the Equal Protection clause. The argument for Virginia was that because a Legislature is not psychic and there were so few Asians in the state at the time of the writing of the law they should not have had to contend with that set of circumstances, and that since both white and non white were punished equally it was not biased the Court took a dim view of that argument.