They are in love like heterosexuals and want to be married because they want to be monogamous. Just like heterosexuals they want to say their vows for life to each other and try to stick it out together "until death do you part."
Also, and most important, they want to enjoy the same legal rights and protections as opposite sex couples in a loving, committed, long term relationship. Many people do not realize, or recognize, that in the United States, marriage is a civil legal status. Many different officials are allowed to perform marriage ceremonies such as justices of the peace, ship's captains, judges, clergy and any private citizen who applies for a one-day permit in many states.
However, the marriage cannot take place unless the couple has applied for and received a civil marriage license which the person who performs the ceremony must sign. It should be noted that a promise to have children is not a legal requirement (or prerequisite) of obtaining a marriage license and many legally married people choose to not have children.
As a gay person legally married to another man, we chose to enter into a civil marriage for the same reasons heterosexual couples marry: we love each other and want to provide our relationship with the legal protections civil marriage provides. (For example, the right to make medical decisions for each other in the event one of us cannot decide for himself; assurance that when one of us dies the other will automatically have the rights of a surviving spouse.)
We have "benefited the State" by remodeling two houses and paying the increased property taxes on them; by being gainfully employed (more taxes); by participating in government at all levels, etc. just like heterosexual couples, including those without children.