fixate

Concise Oxford English Dictionary © 2008 Oxford University Press:
fixate /fɪkˈseɪt/

▶verb

• 1 (often be fixated on) cause to be obsessively interested in something or someone.

  ■ (in Freudian theory) arrest (a person or their libidinal energy) at an immature stage, causing an obsessive attachment.

• 2 direct one's eyes towards.

– origin C19: from L. fixus, past part. of figere (see fix) + -ate3.