Based on the rhetoric in the passage, the impact Wilberforce is hoping to have on his audience is that he hopes they will support abolition.
This can be inferred from his emphasis on presenting his argument rationally and systematically, appealing to their reason rather than emotion, and his conviction that they will eventually be united in their stance against the slave trade. He expresses a desire for the House to deliberate thoughtfully on the matter, suggesting that he aims to persuade them to recognize the moral imperative of abolishing the slave trade.