Let's take a look at the following sentence -
It's got nothing to do with you
I believe you understand the tense being used here and the grammatical structure of this sentence, so I am not elaborating on that. Now, let's modify the sentence just a bit -
It's got nothing to do with your car
Does this make sense? Your car in this sentence is the object of the sentence, your is the possessive pronoun that is merely there to provide us information about the car that is the real object here but that needs to be qualified with your. Since it's not a general car we are talking about here; we are talking about your car.
Now, let's modify it a little again -
It's got nothing to do with your driving.
Similar structure like the last sentence. Car has been replaced by driving which, just like car in the last sentence, is a noun (it's called a gerund and is obtained by adding ing at the end of a verb). But your driving is the object of the sentence.
Let's modify the sentence once more, just a little -
It's got nothing to do with your being blind
Well, this is how the sentence you wrote should've been structured, if one went by the strict norms of the English grammar. And in this structure, I believe it is evident that your being blind is nothing more than the object of the sentence and being blind is working as a noun, like car or driving. Being in this sentence is working as a gerund which is obtained by adding ing to the verb 'to be'. As mentioned by others in the comments, another way to structure this sentence can be -
It's got nothing to do with the fact that you are blind.
In which case we replace the gerund or the noun form of 'to be' (being) with the verbal form (are).
Edit: Adding an additional line of explanation in light of the conversation that happened in the comments. It's got nothing to do with you being blind can be deemed correct as well. 'Your' is the grammatically correct option and if one wants to follow the norms of the language, one should use 'your' only, but 'you' has become colloquially accepted at a wide scale and so, in day to day speech and in fictional works, 'you' is used almost exclusively. But that doesn't change the fact that grammatically 'your' is the right pronoun to use.