The character who says those lines is Catherine Earnshaw.
Explanation:
The lines in the question were taken from Chapter 15 of the novel "Wuthering Heights" by Emily Bronte. The character who says them is Catherine.
At this point in the novel, Catherine is suffering from a strange illness, something that affects her both mentally and physically. As we know, the novel revolves around the unfulfilled love between Catherine and Heathcliff. It is as if that lack of fulfillment is now taking its toll on Catherine's health. In those lines, what she expresses makes it seem as if she is ready to die, as if she is tired of this world and longing to be in Heaven, in peace. That would make sense, after all she has never had peace in life.
