Most properly, it should be "I want that too" or "I want to marry you too" or "I feel the same way." Saying "me too," although OK, makes it sound strange, in my opinion. It sounds like you're saying "I also would want to marry me" (myself!).

I agree with Eric. Both "me too" and "you too" sound strange in this context. You could say "I want to marry you too."

The answer should be: "me too".