All the answers here are correct, that it means they don't want to be forced into it. There is a slight inference in it that they DO want to marry you, but they don't want it to feel forced (an obligation).

I guess it means that the person don't want to be forced to marrying you.

To answer the question fully. The preceding conversation is need, if there is or was any. It could mean many things. Have to means must either by force or by social convention / ethnic convention or possibly for some other reason Your sentence: "I don't want to but I have to marry you". Is implying they must marry because either social moral convention / ethnic convention/ or religious convention dictates or they are being forced to for whatever reason

What's the situation? Have to means no other choice, but there are many types of situation, including joking. Eg: You really want to get married. I promise to marry you if you don't find anyone.. But, I hope you find someone!.. (otherwise I'll have to marry you!) :)

"I don't want to have to marry you" Means that the person who has said it doesn't want to marry 'you' against their will.