Vex:
1: To bring trouble, distress, or agitation.
2: to bring physical distress to.
3: To irritate or annoy by petty provocations.
“I fret about nothing on earth except papa’s illness,’ answered my companion. ‘I care for nothing in comparison with papa. And I’ll never—never—oh, never, while I have my senses, do an act or say a word to vex him. I love him better than myself, Ellen; and I know it by this: I pray every night that I may live after him; because I would rather be miserable than that he should be: that proves I love him better than myself.” (Brontë 200)
Around this quote there are several very important events that are taking place. To start Edgar has become very ill and the possibility of his death is very high and near.