If your answer to Heathcliff's character development as seen in Chapter XI is based on the text, there can be only one answer. That answer is that Heathcliff is clearly not at all a sympathetic character and clearly entirely a villain.
(1) The passage that leads into and introduces Heathcliff's role in Chapter XI describes Heathcliff in the most villainous terms:
His visits were a continual nightmare to me; and, I suspected, to my master also. His abode at the Heights was an oppression past explaining. (Chapter X)
(2) His behavior in accosting Isabella the way he does is completely villainous, especially after, as Nelly explains, having told Isabella he hates her. (3) His treatment of Catherine, arguing with her in her own home, in her own kitchen, after welcome had been extended, shows his villainousness. (4) Nelly's reaction to his behavior toward Isabella and Catherine makes it clear the she thinks he is a villain, and Nelly is the voice of mental stability in the story, which is one reason Brontë uses her as the narrator. (5) Heathcliff's declaration of of revenge marks him as a villain:
[Catherine] you are an idiot: and if you fancy I’ll suffer unrevenged, I’ll convince you of the contrary, in a very little while! (Chapter XI)