You are not helping people because of their race, so why use that to select who gets help? There are rich black people as well as there are poor white people.
Think of this mathematically. We did something very wrong at time T = 0. It is a matter of fact that economic wrongs are self-perpetuating and long-lived. Thus, at time T = 450, you can isolate, statistically, some economic disadvantage in any black person who can trace their lineage back as being affected by that original wrong at T = 0. It doesn't matter how rich they are--they would be incrementally richer had that wrong not occurred.
At the same time, the poor white person benefited from that original wrong, and you can isolate, statistically, some economic advantage to him tracing back to that original wrong. It doesn't matter how poor he is, he would be incrementally poorer had that wrong not occurred.
The harms and benefits you are talking about are not quantifiable in a commonly-agreed-upon way. I think that's a prerequisite for the kind of analysis you want to do.
At the same time, the poor white person benefited from that original wrong, and you can isolate, statistically, some economic advantage to him tracing back to that original wrong. It doesn't matter how poor he is, he would be incrementally poorer had that wrong not occurred.