The answer to this question can be found in Chapter Ten of this excellent novel. Isabella, having confessed her feelings in a very petulant manner to Catherine, then has to endure the shame and embarrassment of Catherine revealing them openly to Heathcliff when he enters the house soon after to be shown in to a room with both Catherine and Heathcliff in it. Note how Catherine greets Heathcliff:
"Come in, that's right!" excalimed the mistress, gaily, pulling a chair to the fire. "Here are two people sadly in need of a third to thaw the ice between them; and you are the very one we should both of us choose. Heathcliff, I'm proud to show you, at last, somebody that dotes on you more than myself. I expect you to feel flattered... My poor little sister-in-law is breaking her heart by mere contemplation of your physical and moral beauty."
Thus it is that Catherine is the one to tell Heathcliff of his ardent admirer. She does this of course with the chief intention of showing Isabella how ridiculous the idea of her union with Heathcliff would be, but actually she underestimates Heathcliff and his desire to gain revenge.