The royal lady is the victim, right? It's her letter that's stolen; she's the one being blackmailed.
Well, let's not take it for granted.
Most people assume she represents a queen of France sometime between 1800 (the story is set in 18— in France) and 1844 (when the story was published). But she could just as easily be some other member of a French royal family, or, hey, she could even be a non-royal gal. We only have G—'s word for it, after all. Still, we'll go with the obvious answer: the queen is a fictional queen made up extra-special for the story, but she can serve as a comment on queens everywhere.
Sure, she might be a victim of corrupt political forced—but, frankly, it seems just as likely that she's deceitful, irresponsible, corrupt, and impressively powerful.
We don't know why, but we do know that it was the lady's "wish to conceal" (28) the letter from the royal man. Furthermore, if the royal man (and presumably the public as well) learned what's inside the letter, they would "question" her "honour" (26). Most readers assume that the person writing her is a lover. (We know the letter is from a guy, because Dupin suggests that the handwriting on the letter is a man's handwriting, calling it "bold and decided" in contrast to the fake letter's "diminutive and feminine address" .)
Look, we're not offering an opinion on the queen's affairs, legitimate or illegitimate. Still, we want to point out that she's probably using money that rightfully belongs to the people of France to cover up her affair; she's also taking valuable time and manpower away from the police force; and she's apparently compromising her political ideals in order to keep the business quiet.
G— tells Dupin and the narrator that "the power thus attained has, for some months past, been wielded for political purposes to a very dangerous extent" (30). In other words, she's doing things that might be bad for the people of France. How much of a victim is she, and how much is she actually more of a villain?
But we have to acknowledge that G— makes the royal lady look like a victim. Dupin seems to agree with his assessment. When he finishes telling the narrator how he took the letter from D—, he says, "In this matter, I act as a partisan of the lady concerned. For eighteen months the Minister has had her in his power. She has now him in hers—" (120). Because we see her through the eyes of Dupin and G—, we tend to want to agree with them.
Plus, blackmail and theft are pretty low. A lot of people would say it's much uglier to blackmail someone than to take a lover. Plus, we don't even know for sure that it's an affair. Maybe she's planning an awesome birthday party for the king, and she really, really doesn't want to spoil the surprise. Or maybe she's covering up someone else's affair.
The point is, Poe is playing on the fact that most people would agree that taking a letter is worse than almost any other crime. Even the U.S. government agrees: stealing mail is a federal offense. We want to see things in their rightful place, so we're really rooting for the letter to be found.
Also, the queen is obviously not fully on top of this situation. D— must have something on her, because why else wouldn't she just have said, "Oops. Looks like you picked up my letter by mistake"? Since the king doesn't notice anything else, it seems unlikely that he would have noticed that.
In fact, the king seems pretty oblivious. D— can read her like a book, but her husband, who is "at her elbow" (28) doesn't notice that something's up with her. The blackmail goes on for a year and a half and he still doesn't find out. He doesn't even notice that his police force has been engaged in a mysterious nightly search, not to mention that the king hasn't picked up on the fact that there's some hinky political maneuvering going on, and, gee, the queen sure does seem a little stressed these days
Yeah, no wonder she's receiving secret letters.