There are several possibilities. I think that the most likely are that:
the first is a proposal of marriage;
the second could be a question about whether an already arranged marriage will take place - Last week you said you wanted to call it off; on Monday you said you were looking forward to it. Now you're getting cold feet again. Make up your mind! Will you be marrying me or not?
´Will you be marrying me?´ Possibly Irish English, or as fivejedjon said, from the context it could indicate choice: 'marrying me or not?' 'marrying me or him?'