How does Browning portray the Duke in "My Last Duchess" as weak?

The Duke is so insecure that he needs his spouse to acknowledge him as the best and most important thing in her world. He says,

'twas notHer husband's presence only, called that spotOf joy into the Duchess' cheek.

He wants her to blush for him and for no one and nothing else. Instead, however, of overtly recognizing his importance in her life, the former duchess was "Too easily impressed": she appreciated his "favour at her breast" as much as she did a bough of cherries brought to her from the orchard, or the white mule she rode on, or the sunset. She did not stroke the duke's ego. She simply took joy in everything and anything, rather than explicitly and only in his "gift of a nine-hundred-years-old name." He admits that he could have instructed her, told her how he wanted her to act, but he says that this would amount to "stooping; and [he] choose[s] / Never to stoop." In other words, he thinks that it would be beneath him to have to explain why she should favor him the most, and he would never lower himself to do such a thing. We see his weakness here. Rather than confront his wife and speak to her about his wishes, he chooses to have her killed: he "gave commands" that made her smiles stop altogether. He cannot stand his own insecurities or love anyone more than he does himself. He cannot even have an uncomfortable conversation, because he lacks the strength.