According to the Merriam Webster Dictionary, "sympathetic" means
feeling or showing concern about someone who is in a bad situation : having or showing feelings of sympathy.
If that is the case, Arthur Dimmesdale does not seem to be at all sympathetic in Nathaniel Hawthorne's The Scarlet Letter. In fact, he seems to be just the opposite: unsympathetic.
The first time we meet Dimmesdale is at Hester Prynne's public punishment on the scaffold. This most pious minister is standing above her, looking down on her along with the rather haughty Reverend John Wilson. It is true that Dimmesdale does not condemn Hester the way Wilson does in his sermon against adultery; however, he obviously does not do the one thing he could do to show sympathy for Hester. He does not reveal that he is the father of her child and her fellow adulterer. Instead he allows her to suffer her shame alone. That is not a sympathetic act.
Later in the novel, both on the scaffold and in the forest, Pearl senses the connection between her mother, Dimmesdale, and herself, and she asks Dimmesdale if he will stand with them publicly. He denies her request and even, by omission, denies his true relationship to the girl. Pearl's father refuses to acknowledge her except under the cover of isolation or darkness. That is not a sympathetic act.
While Dimmesdale's congregation seems to think their beloved minister can do no wrong, in fact is a man sent to them directly from heaven, he essentially lies to them. It is true that he does passionately admit to being a sinner; however, he is not specific about his sins and knows perfectly well that his "confessions" will actually make him seem even more pious to them. This is an act of deliberate hypocrisy, not an act of sympathy.
When Dimmesdale comes back into town after making plans with Hester in the forest, he is tempted to do very unkind things with several people in his church, including telling a little old widow, whose only hope is that one day she will be reunited with her loved ones in heaven, that there is no such thing as eternal life. That is not a sympathetic act.
I think you get my point. Now, if perhaps you meant that he is a man who deserves our sympathy, you might have a more valid point. The inescapable truth, however, is that he created his own problems and then deliberately chooses not to do what, as a man of God, he knows he should do: confess his sin and repent. To avoid God's punishment, he punishes himself. I find it difficult to sympathize with someone who creates and then perpetuates his own bad situation, especially when he knows how to make things right.
Throughout the entire novel, Dimmesdale thinks only about himself. Truly. Perhaps the best "-etic" word for Arthur Dimmesdale, then, is pathetic. It means
very bad, poor, weak, etc.
Arthur is weak and frail physically and he is crippled emotionally by his guilt. He has nothing to give other people because he has to spend what energy and life he has on himself; he is essentially self-absorbed and selfish. That is the opposite of a how a sympathetic person lives his life.