Preoccupy (6)
'preoccupy' is the definition.
(obsessing is a kind of preoccupying)
This is all the clue.
(Other definitions for obsess that I've seen before include "Plague" , "Prey on" , "Persistently preoccupy" , "Preoccupy continually" , "Constantly worry (about something)" .)
(Other definitions for fixate that I've seen before include "Become absorbed" , "Obsess (on something)" .)