What do you think the Duke feels about his late wife when he says "She had a heart-how shall i say? - too soon made glad / Too easily impressed: She liked what'er / She looked on, and her looks went everywhere"?
The narrator/Duke is obsessed with his title, his self-importance. He does not think that his “last” duchess gave his station enough importance; he is disdainful of her indiscrimant joy, and feels that she was too easily flattered and grateful for the small attentions given to her in their everyday life. He is particularly upset by “the bough of cherries (blossoms) some officious fool” gave her in the garden – he felt that this insignificant gift gave her as much pleasure as his “gift” of the title of “duchess” – “too soon made glad”. This resentment, together with his other traits of treating her not unlike his statues and other possessions, reveals to the reader the real “character” of the Duke. It is not so much sexual jealousy as social jealousy, although the mention of Fra Pandolf's flirtatious comment hints at it (until you note that this artist is a monk, hardly a flirter). She is not sufficiently haughty or snobbish for him.