Answer:
There is some indication in this expression of the Duke's grievance as to why he did not actually express his displeasure to the Duchess. He is a proud man and feels that to criticize such "trifling" misbehavior on the part of the Duchess would be "some stooping; and I choose / Never to stoop." The Duke realizes that his complaints, while valid to him, might seem petty to others and that if he should object, it would belittle him in the eyes of the Duchess and others.
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