To what degree should we regard "hate" as an emotion with strong significance?
You have raised an interesting discussion. I am not sure that the feeling of strong dislike and feeling hatred and that of wishing harm is absolute. Perhaps the latter is the exaggeration form of it and most people don't go that far. It could be that the more a person becomes accustomed to the mental state of feeling and thinking thoughts of aversion or hatred, that it becomes a possible starting point is hatred, in its meaning of wishing harm.
I think that hatred, in strong aversion or wishing harm to those with specific attributes is connected to psychological projective processes. Take your example of hatred of the fat person, it may be that specific undesirability of fatness as an aesthetic quality is projected onto the individuals who are perceived as fat. The example of hatred of fat people also raises the connection between hatred of others and hatred of self. I have worked with people who have eating disorders and it does seem that they often have internalised self hatred.
The whole area of self hatred is also of importance in thinking about individuals who self harm. I have heard people who harm themselves in ways such as cutting saying how the cutting is a way of purging themselves of the anger and hatred they have towards themselves. The whole area of self harm was expressed strongly in the culture surrounding 'emo' music culture. I think that emo culture is less strong now, but it is often during adolescence that people experience strong feelings of self hatred, and this is probably related to the sense of identity development. However, many people in adulthood do self harm and experience suicidal ideas in adult life.