What did Gene mean when he said that he and Finny were "even in enmity" or in fact that the scales were even tipped in his direction?

In context, we see that Gene feels the rivalry between he and Finny is equal on both sides. He projects his own envy and dishonorable actions on Finny and believes this justifies his own reactions. Unfortunately, Gene is wrong.

As for the second part of your question, Gene feels himself superior to Finny. Finny is great at sports and a horrible student. Gene, on the other hand, is fairly good at sports and a great student. In Gene's eyes, this gives him an edge.