Though he's a conservative, he has a long history of voting in favor of gay rights, placing him as leaning socially libertarian. Throughout the court proceedings he has treated LGBTQ people with respect and dignity. I believe he will, if reluctantly, come down on the side of universal marriage rights.
Justice Kennedy will vote in favor of same-sex marriage. Although he does lean conservative, Kennedy has a pattern for backing equal rights for same-sex couples. He doesn't feel there is a moral imperative to restrict marriage to opposite sex couples. He also says in the article that straight couples having a greater bond with their children is the "wrong premise."
In the upcoming Supreme Court decision regarding whether or not states can ban same-sex marriage, Anthony Kennedy will vote that same-sex marriage is constitutionally protected. This is consistent with his track record, having previously voted to shut down the Defense of Marriage Act (DOMA), and believes that the dignity of marriage is a right to all people, including gay couples.
It is unfair to regulate who can get married. Multiple states have come to this realization. It has become obvious that the majority of the country doesn't care who you choose to sleep with regardless of their sexual orientation. Most of the country wishes this vote would go ahead and pass so we can move on to important issues.