Montresor claims that Fortunato has one "weak point" and this is that he "prided himself on his connoisseurship of wine." Pride, in general, does seem to be Fortunato's weak point; he thinks highly of himself, and he seems to feel somewhat entitled -- even his name means fortunate one! It is this quality of Fortunato's that Montresor can use to manipulate him, and his pride, itself, will actually prevent Fortunato from realizing that he is being manipulated by Montresor.
One of the ways that Montresor manipulates Fortunato by using the man's pride against him is by being somewhat self-deprecating and then admitting that Fortunato is more qualified than he on the subject of wine. Concerning the supposed pipe of Amontillado, Montresor says, "'I was silly enough to pay the full Amontillado price without consulting you in the matter [...]." He implies that he behaved hastily, without due reflection and consultation, and that he would have been smarter to have gotten Fortunato's opinion before he purchased the wine. Montresor knows that Fortunato will not be able to resist the opportunity to gloat over Montresor's mistake.
Likewise, as the two men descend into the catacombs, Montresor repeatedly insists that they should turn back for the good of Fortunato's health. The walls are crusted with nitre (potassium nitrate) which makes it difficult for Fortunato, who is already somewhat ill, to breathe. But Fortunato seems not to want Montresor to be right about anything, and so he denies, over and over, that he is suffering. Moreover, Montresor tells Fortunato, "You are rich, respected, admired, beloved; you are happy, as once I was. You are a man to be missed. For me it is no matter." Again, Monstresor speaks slightingly of himself in order to flatter Fortunato's pride, and so Fortunato, proudly, rebuffs Montresor's expressions of concern.