I disagree wiht you betting this river. Anyone that will call will likely have you beat in this situation espeically since u are first to act. Any straight will definately raise, although i dont see how the button would check the turn with a straight.

Lastly, if you fold this river, it is unliekly that he has a set because he would generally not raise with a set with this board.

Check call especiially from the button bet would be appropriate.