Answer: C. That he is possessive and controlling.
Explanation: The speaker in this poem is not Browning himself, but the Duke of Ferrara, talking about a portrait of his deceased wife among other artworks in his collection. In his recollection of her, he recognizes he was not fond of seeing her smile for other men, and now that she was dead (we are lead to suspect he had her killed), he makes sure she only smiles for him by controlling this curtain.