Godfrey is the eldest son of a powerful man who is a landowner, runs the Red House estate, and is rich under the parameters of a small town such as Raveloe.
This being said, it was expected for a man of such social consideration to be in search of a wife, since wives were one of the many "acquisitions" a man who will come to property is supposed to get.
However, Godfrey is weak of character, weak in morals, and weak in leadership. He is nowhere near as talented as his father in attaining success, and he is also consistently a pushover of his brother.
Unfortunately also for Godfrey, a good match that could have occurred with another rich heiress in Raveloe could not happen because earlier in his youth Godfrey was lured by a low woman whom he ended up marrying and having a child with ... in secret. So, basically he has ruined himself socially being unable to consecrate a good marriage, and for hiding the reality of his hidden life.