The antagonist of a story is whoever or whatever is trying to keep the protagonist from fulfilling his goals. And, since Arthur's goal seems to be to wrap up his job in Crythin Gifford as soon as possible so he can go marry Stella and have a beautifully domestic life—that would make the woman in black his antagonist. Major antagonist. She manages to destroy Arthur's family and innocence without even lifting a finger. What a jerk.