"Normalizing" has several different meanings and one of them is sociological. You can find many complex meanings, but one of the most simple ones is that it is the process of making something seem natural, logical, and commonplace. The word carries no value judgment about what is being normalized, and the act of doing so should be seen as a logical and expected part of the changes to culture.
That is not to say that "normalizing" is always a positive thing in the minds of everyone who witnesses it. One of the biggest examples of normalization which has been successful and ongoing over the past half century has been the perceptions of homosexuality. In my lifetime, I have seen the normalizing of it by society in action. What was once considered deviant and abhorrent is closing in on being considered normal and mainstream. For those (like myself) who believe that homosexuality is a biological inevitability and that sexuality is not a "choice", this is good news as we view it as the end of an unfair and oppressive environment. For those who have philosophical objections and believe a true choice is being made, this particular type of normalization is upsetting and unacceptable. They feel it is removing restraint from behavior that should be held in abeyance.
Normalization comes as a result of a great many factors. One is technological advances. Another is scientific discovery. Yet another is the evolution in philosophies based on education and integration of new ideas. Very generally speaking, there is a movement in most cultures toward more liberal thinking. That is, this is the direction until there is some shift back toward conservatism based on hardship. Those difficulties can be economic, medical (such as the outbreak of disease), or brought on my aggression (e.g., war).
All normalization is resisted by a certain segment of any society. When those views act in opposition to yours, it is easy to see them as small-minded, irrational, and selfish. When they agree with your views, they seem to be "right-minded". It's hard not to apply value judgments to both sides of the equation when it comes to normalizing of behavior, but it is important to understand and accept that the perspective of others has some validity. Dismissing alternate views out of hand lowers the quality of discourse and encourages rigidity on both sides.
With this in mind, I've been pondering both sides of the equation when it comes to the fat acceptance movement's efforts to normalize widespread occurrence of obesity. As someone who has spent her entire life overweight, and the vast majority of that life over 300 lbs., I know all too well the damage that is done to someone based on body judgment. I strongly believe that punitive attitudes toward fat people only do harm whereas people who fear the normalization of fatness as an endorsement of what they view as a "fat lifestyle" and what they often erroneously conclude is sloth and gluttony believe that social censure will increase the chances that people will not engage in behaviors that result in obesity.
Unfortunately, having lived a fat life, I also know that normalizing (as opposed to accepting, which is a whole other kettle of fish) obese bodies isn't necessarily a good thing on some levels. For one thing, accepting that being fat is expected, normal, and "usual" means that people will not attend to it based on health concerns. Despite all of the HAES propaganda, being obese (as opposed to merely "overweight") will eventually impact your health. You'll find that there are few fat advocates out there over 40, and even fewer over 50, who will latch onto the notion that being obese doesn't mean being unhealthy.
When I was younger, my body dealt a lot better with obesity than it has after 40. I'm now 47, and I have the joints of a person much older than me because of the extra pressure that has been on them for so many years. I'm not sure how anyone can say in good conscience that carrying 50-200 lbs. of extra weight will not take a toll on ones joints eventually. There is also the fact, and fat advocates are in denial about this, that pressure on the glands affects type 2 Diabetes development. Weight gain can bring on this condition and loss can send it into remission. That is not to say that one does not have to be genetically predisposed to develop it, but simply that it is a fact that weight affects development of such a condition.
Because of the health issues associated with obesity, normalization of fatness is a more complex issue than other social issues, trends, and concerns. On the one hand, fatness needs to be accepted because fat prejudice is unjust and highly destructive. I am certain that, had I not been tormented as a chubby child, I never would have grown up to be an extremely obese adult. It was the disapproval which sent me from overweight to class III obesity. Dehumanizing a group of people based on superficial characteristics serves only to create a loop of neurotic behavior which creates conditions that encourage eating disorders, including compulsive eating, overeating, and binge eating. As a psychological and social issue, fatness needs to be normalized and what I mean by that is that it needs to be regarded as a normal state for some people and they should not be treated with prejudice.
On the other hand, however, normalization which discourages people from dealing with their weight when weight will affect health (which is certainly the case for many people who are obese, especially in class 2 or 3 obesity), mobility, or quality of life (especially mentally) isn't such a great idea. While I fervently believe there are some people who were "born to be fat", it is undeniable that more and more people are fat and getting fatter compared to the past. If being fat were a normal human condition brought on by genetic predisposition, we wouldn't see the recent increases in the number of overweight people nor an increase in the amount of weight they gain. I realize that BMI was shifted to statistically move a great many more people into the "overweight" category, but that does not account for the dramatic increase in obese people and especially the super obese (such as I once was).
The issue with normalization and obesity needs to be split between societal and philosophical acceptance on the one hand and medical attention which indicates it is to be viewed as an undesirable condition on the other. In societies in which fatness is seen purely as a bodily issue related to health (there are some, but just not in the West) rather than a moral or character failure, people address their weight the same way that they do other factors which affect health. If someone is anemic, has poor circulation, etc., the measures taken to look after their body given these conditions are not seen as oppressive or unfair. They are simply seen as what is necessary. The same applies to weight in such cultures. I know because I live in such a culture at present. Fatness isn't about morality or character, but about health. While I don't believe that anyone is required to be healthy, I do believe society should encourage people to act in a manner which promotes happiness and the highest possible quality of life. And if you are not healthy, you will not have a good quality of life. Do we want to normalize conditions which decrease quality of life? I don't believe this is good for society on the whole, let alone the individual.
Unfortunately, the prejudice and venom directed at fat people that society is currently indulging in is what encourages more extreme and broad efforts to normalize obesity. The harder you push people, the harder they will push back. It is similar to the way in which the NRA pushes to keep extreme weaponry legal in order to make sure they can keep their hunting rifles and hand guns.
The answer is simple, but people are reluctant to take it because they have to change their personal slant to a more objective one. Stop judging and abusing people based on their bodies. Stop encouraging the false notion that health and weight are completely different factors for most people. Deal with this like adults without injecting value judgments or personal opinions. As is so often the case, I'm not holding my breath.