It depends on who exactly they kill, or what they empathize with. They might start out as a very sensitive character who can’t bear to pick up a flower, so it doesn’t even have to be a murder. The more they do it the more fucked up they become but if the fifth murder is a loved one, it’s more morally reprehensible, or depending on their moral compass, a child, an old person, a woman, a teacher, a cop, all this can skew the balance either way. So, in general, yes, but not always

It should be a power where the more morally reprehensible thing they do according to their own compass, the more powerful they become

It’ll be awesome to see a hulked out trolley man, distraught, eyes clouded with tears, his friends asking them “what did you do ?”. Then they’re sent flying by trolley man simply turning their head toward their friends. Trolley man can’t even say they’re sorry, it’ll probably rupture their eardrums on the spot.

Trolley man is on the brink of losing it all, it would only take one last kill for them to become an uncontrollable natural disaster, feeding their curse.

Obviously the villain shows up.