What's there to say about Jack Durbeyfield? He's a minor character, but like Mrs. Durbeyfield, he serves a certain purpose in the novel. His unreasonable pride in his dusty D'Urberville connections makes him even more unwilling to work than he was before. In fact, his character can really be summed up in two words: pride and shiftlessness. The narrator frequently describes him using the word "shiftless," which is really just a synonym for lazy: for example, as the head of "the shiftless house of Durbeyfield" (3.40).
But despite his flatness as a character, he's still important to moving the story forward: when Parson Tringham calls him "Sir John," and tells him that he's a descendent of the ancient D'Urberville family, Jack Durbeyfield becomes absorbed in this illusions of grandeur, and starts puffing himself up because of his ancestors. He's just the kind of "aristocrat" that Angel later criticizes – the sort that values noble blood in a person for its own sake, regardless of the actions or worth of the person.