In Browning's poem, "My Last Duchess," the Duke was married to his lovely wife, the Duchess, whose painting he has on the wall of his castle and is showing it to a visitor. As we read the poem, we find out that the Duchess liked to flirt a lot with other men which is why the Duke had her killed. I'm not sure who Browning seems to sympathize with - I guess the Duchess, given that she was murdered. The Duke is not the one who should be sympathized with.