cathect \kuh-THEKT, verb:

To invest emotion or feeling in an idea, object, or another person.

Yet such sympathy becomes forceful through mass-cultural stereotypes, visceral and imaginative figures of woman as demon with which readers can easily cathect.
— David Bruce Suchoff, Critical Theory and the Novel

We cathect something whenever we invest emotional energy in it, whether that something be another person, a rose garden, playing golf, or hating lessons.
— Morgan Scott Peck, Golf and the Spirit

Cathect is a backformation that emerged in the 1930s. It comes from the idea of cathexis from Sigmund Freud’s term for emotional investment.