I suppose the question should be "When you're white, the sky' s the limit; when you're black, the limit' the sky?"
Since I have not watched that movie, I don't know what "white" and "black" are referred to under that particular circumstance.
But I think "the sky's the limit" means nothing is impossible and one can chase dreams, seize the opportunities and his fate is in his own hand while "the limit's the sky" means the opposite situation.