It definitely is an esteem-issue, and you're right that it can also be a form of manipulation to try to get a stream of compliments and reasurance out of you. Have you tried reversing the questions onto the person? When they ask if they're too fat, you ask them "well, how do you feel about that?" - it may force them to confront their own feelings that they are trying to avoid by constantly seeking reassurance from you.

Does the other person suffer from any form of mental illness? That would be another story (and a whole new case of cans of worms).