What's the noun for empathising? Here's the word you're looking for.
empath
One who has the ability to sense emotions; someone who is empathic or practises empathy.
(science fiction, parapsychology) A person with extra-sensoryempathic ability, capable of sensing the emotions of others around them in a way unexplained by conventional science and psychology.
“For example, the theory approach emphasizes the cognitive inferences involved in the process but fails to address the emotional state of the empathizer.”
“The inhibited empathizer is afraid to get involved with the patient.”