why won't the state allow close relatives to marry?
Actually, it will, depending.
Here's a good quick view from a Wiki article, of all things:
"In the United States, every state and the District of Columbia have some form of codified incest prohibition.[30] However, individual statutes vary widely. Rhode Island repealed its criminal incest statute in 1989[30], Ohio only targets parental figures[30], and New Jersey does not apply any penalties when both parties are 18 years of age or older.[30] Massachusetts issues a penalty of up to 20 years' imprisonment for those engaging in sexual activities with relatives closer than first cousins[30] and Hawaii up to 5 years in jail for "sexual penetration" with certain blood relatives and in-laws.[30]
In all states, close blood-relatives that fall under the incest statutes include father, mother, grandfather, grandmother, brother, sister, aunt, uncle, niece, nephew, and in some states, first cousins, although Rhode Island allows uncles to marry their nieces if they are part of a community, such as orthodox Jews, for whom such marriages are permitted. Many states also apply incest laws to non-blood relations including stepparents, step-siblings, and in-laws.[31]
UCLA law professor Eugene Volokh has questioned the rationale behind laws prohibiting incest, at least as they apply to sex between adults.[32]"
:e4e: