You shouldn't have been banned permanently. I think the appropriate duration of ban for that kind of fatphobia is a month.
Scientists have well documented the negative effects of stress and shame on health outcomes. Positive pressure to get motivated and improve one's health can be effective. But mean-spirited speech, insults, and shaming or blaming statements do not, statistically, have positive outcomes. They're more likely to result in stress eating, panic attacks, and depression, all of which increase your risk of heart disease. The idea that fat shaming works is pseudoscientific misinformation, and if you look at the consequences scientifically, it promotes an unhealthy lifestyle. Fat shaming does work for SOME people, but on average, it will make people less healthy. It's not supported by doctors or scientists. They would recommend more positive and encouraging ways to help someone lose weight, not just slinging insults.
So when we're talking about hateful pseudoscience, banning people who engage in that behaviour is appropriate, but I don't think it should be permanent unless you've been fatphobic in the past.
Even if it wasn't hurtful, it was needlessly rude. Fat people are, in general, aware that they're fat. They don't need to be told they're fat. You wouldn't tell someone with a big mole on their face, "go to a dermatologist, mole-face!"