The legality of this varies widely by state. As long as you are both consenting adults and you don't have kids together or try to get married, I doubt there would be any issue. Laws prohibiting safe, private sex acts of any kind between consenting adults are unenforceable.
But if your relationship does not fit into this category, it could easily become a complicated legal mess.
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The occasional marriage of first cousins does not seem to be problematic if there are not too many weaknesses in the extended family. But too much of it seems to multiply inherent weaknesses. It depends too if there is some new blood in the mix or if there has been some fairly close marriage generations before (maybe second cousins) with no new blood (completely unrelated) brought into the mix. I know of one isolated group that has lost a lot of babies, which seems to have been caused by too much "interbreeding." Don't know of any other problems in that group, though it seems like the children don't quite have normal growing vigor. In the United States some states will not give you a license to marry, others do. Some couples simply go across the state line to get the marriage license.