obsedi

The thought is the subject, the person is the object. This is the shape learners get wrong first: in Esperanto la ideo obsedas min, not mi obsedas pri la ideo. If you want the person in front, use the passive participle: mi estas obsedita de tiu ideo. The noun is obsedo, an obsession.

One root, and the seam you can see is Latin, not Esperanto. Obsedi splits neatly into ob- and sed-, and the split is genuine history: Latin sedere means to sit, and sidi in Esperanto sits in the same family. But ob- is not an Esperanto prefix and sed- is not an Esperanto root - the word arrived whole. Worse, Esperanto already has a sed, meaning "but", and it has nothing whatever to do with this. Treat obsed- as one indivisible piece.

The picture behind the word is the useful part. An obsession is a siege: the thought sits down outside your walls and refuses to move on. That is exactly what the Latin says, and it explains why obsedi is stronger than pensi about something and closer to turmenti, to torment.