In Act 1, Scene 1, the Duchess uses hyperbole to express herself to Antonio. She and Antonio have been dancing around their feelings, unable to communicate because of their class differences and the pressure on the Duchess to never remarry. Their relationship hasn’t been made explicit yet, and the pair have been communicating through pun and undertone exclusively. Therefore, when the Duchess finally expresses herself honestly, her exaggerated language makes the confession even more emotionally resonant. She is finally able to say how she feels, and though the situation she describes is an impossibility, her overblown language helps the audience understand the gravity of her confession. She says:
Go, go brag
You have left me heartless! Mine is in your bosom:
I hope ‘twill multiply love there
The Duchess implies that Antonio has stolen her heart and holds it now within his own chest. Although that is not actually possible, her description gains meaning because direct expression was previously impossible. This moment is a revelation for the Duchess. Because of her class, she felt unable to state her affection outright for a long time. Therefore, the emotional crescendo of the scene takes place around this instance of hyperbole. Having communicated through puns and implications, it makes sense that the Duchess would be overcome as she finally confessed the depth of her love and affection for Antonio. Her exaggeration is a symptom of that release, and the audience can feel it and understand it all the better because of her statements here.
