Thesis: Hatred for fat people has the same basic reasoning as hatred for gay people.
To start out, let's ignore the argument that hatred is derived from some sort of natural xenophobia or other arguments of that sort. I'm not saying they're not true, but in this case, they're boring. They cover all hatred. I'm more interested in these two particular forms because they're 'fashionable.'
So let's get to the fun stuff: how they are alike. By they I mean the targets. In the minds of those who hate, how would gay people and fat people be the same? Please remember when I set these up that I am giving stereotypes and perceptions. Some of what I say will be objectively true, some is true but rare, and some is 99% in the mind of the beholder (hater). If I say something blatantly wrong, I probably know it, but wouldn't it ruin the fun if I pointed out every specific flaw?
They look funny
Fat people often have a sort of waddle and generally slow movements. They may have difficulty moving both due to weight and size, depending on the situation. They're easy to identify, easy to point and say: "That person's fat."
Gay people, at least by stereotypes, are much the same. Over the years they've varied, but limp wrists and certain styles of dress, or perhaps more accurately, any style, are stereotypical. They may more with a bit of a flourish, an expression of energy that you won't usually find in everyday interaction.
In short, they're identifiable, noticeable for not looking right.
Science says they're wrong
Fat people are a burden on all of us. They get sick and wreck our healthcare system. They're not natural they way they eat and eat and eat and never exercise. They're a disease.
Gay people spread AIDs. They spread disease with their unrestricted and unnatural sex practices. They're unnatural because no species can survive without having sex with the opposite sex.
The Bible speaks against gluttony. It's one of the seven deadly sins. They're slothful and gluttonous and selfish with no self-control.
The Bible tells us that homosexuality is an abomination and God specifically made a man and a woman and told them to go forth and multiply. Gay people don't multiply well.
That's all, folks
Using everything from misuse of science to misuse of religion, an army of hateful people are spreading their message across the world. They want you to think what they think, they want you to hate who they hate, and they're too small-minded to even think of new and interesting ways and reasons to hate, so they dig up the same reason they used last year and slap a new picture on their ads.