From his description of his last duchess, you would think the duke would adore her. She is sweet and kind and easy to please. However, quite the contrary is true of the duke. The following lines describe the duchess' personality as reported by the duke. I have added commentary in bold:

She had
A heart—how shall I say?—too soon made glad,
Too easily impressed: she liked whate'er
She looked on, and her looks went everywhere.
The duke says that she is a happy person and that even small things make her happy. Any small compliment would call a blush to her cheek. BUT according to the duke, this joy in small things was a fault.
Sir, 'twas all one! My favour at her breast,
The dropping of the daylight in the West,
The bough of cherries some officious fool
Broke in the orchard for her, the white mule
She rode with round the terrace—all and each
Would draw from her alike the approving speech,
Or blush, at least....Somehow—I know not how—as if she ranked My gift of a nine-hundred-years-old name
With anybody's gift.

The duke is upset that everything pleases the duchess. She is too innocent and too generous with her approval and too easily impressed. He later says that her holding any kindness in equal standing with his affection and his gifts "disgusts" him, though he refuses to "stoop" to tell the duchess why he is upset. She should know without his telling her. The duke thinks that the duchess did not show him the proper amount of gratitude for his granting her his name. He fails to see the beauty in her sweetness.