Born into a rich family and having been spoiled by his father, Godfrey grew up as a reckless, irresponsible young man. All his needs was provided by the servants, no effort was required from little Godfrey. And whenever he wants something, all he need to do is asking his papa, and he will (happily) grant it. He grows up knowing that his part in this world is just wishing, and it's everyone else's job to fulfill. It's all about "me", and never "you"; least of all "he/she", because he has the privilege. It's not his original character - we will learn this later - but it's the way he was raised. Though he might have had moral education from his governess or private teacher, I think emphaty is not something he is familiar with. Why, taking feels much better than giving, anyway!
I imagined Molly is one of the pretties working girls in Raveloe, and young Godfrey is attracted to her. He marries her (clever of you, Molly, at least you've got him legally married you!), though he doesn't have plan to provide for her, least of all acknowledge her (I really wish Eliot wrote more about this!). Anyway, Godfrey doesn't even think it wrong to woo a middle class girl after abandoning Molly. He simply doesn't think his first marriage as marriage; for him it's just a pleasure, and now, an obstacle to his present wish: Nancy Lammeter, or just an annoying subject to get scolded by his dear papa. Godfrey's comfort and pleasure must come first!
Then, Molly's corpse is found, and Godfrey realizes for the first time, that his past reckless act DID have consequences: his own daughter Eppie. I think this revelation is his first turning point. How often is it that a man changes to the better after the birth of his child? So Godfrey, too, starts being responsible and a little more generous, by giving some money to Silas Marner (for Eppie's sake). Unfortunately he is still cowardly and indecisive enough to confess the truth to Nancy.
The revelation of Dunfrey's death shatters Godfrey's last door to self-denial. Without further doubt, he confesses everything to Nancy: first marriage, child, and all. Lastly, Eppie's rejection of living with him, shatters the last of the remnants of his ego. Godfrey is humbled by his daughter! After this last event, we do not know clearly how Godfrey's live has become, only that he contiunually provides for Eppie and Silas. He even pays for Eppie's wedding party, though he doesn't attend it. This is a big change in Godfrey's character. The selfish, egocentric young man has transformed into a selfless matured man, who still loves, cares, and provides for his daughter, despite of her rejection, despite of his realization that Eppie would never be his. We know that at the end of the story, Silas, Eppie, and her husband Aaron live a happy life. I wish Godfrey too, find love, solace, and happiness with Nancy. He deserves it, because after all, he was born as a good natured person.