How did Eric try to redeem himself after he learnt of Eva's pregnancy, and what does this show of his character?

Eric offered to marry Eva, but she refused based upon the fact that he did not love her. He then gave her a bit of money, unfortunately, he'd stolen the money from his father's business..... uh oh.

This shows that although Eric didn't love Eva, he was honorable enough to want his child to have his name.