Imma preface this by saying:
Body shaming in general is bad and harmful to people no matter what. It causes EVERYONE a shit load of problems that we wouldn't otherwise have if people just stopped shaming others for what they look like.
Now that I have that out of the way. The concept of "skinny shaming" is not a thing. Not because shaming people for being skinny isn't a thing, but because you are not socially, or systematically oppressed for being skinny on a wide, general scale.
The same root reason why we generally don't accept the social concepts of reverse racism, heterophobia, cisphobia, misandary, etc. Reverse racism, heterophobia, and cisphobia is what we call prejudice. Misandary is what we call sexism, or if you're me, rewrapped and relabeled misogyny (this is a whole other conversation). And skinny shaming is what we call body shaming.
These majority groups are NOT socially or systematically oppressed. These labels are a social nod to the fact that POC people, 2SLGBTQIA+ people, and women are oppressed in these ways. It is a unique oppressive experience that needs it's own name to show it's importance and unbridled injustice.
Please tell me how skinny people are widely systematically and socially oppressed. Fat is regularly used as a synonym for lazy. You hear someone call another person fat, the vast majority of people will assume they mean to say lazy, unwanted, ugly, unhealthy, the list goes on. You can't even use the word fat in a sentence without people being on edge about the potential horrid things that could come out of their mouth next.
Generally, when you call someone skinny, it's a compliment. When you call someone fat without explicit assurance and permission that it's okay, it's ALWAYS an insult. You can't use the word to describe another person as fat because of the dehumanization that is implied with that word. We use plus size, bigger, whatever. Usually tacked on with PERSON at the end to show you respect them. Same reason why many people tack on person at the end of POC despite the fact that POC stands for person of colour. It's to show that respect.
No, I'm not saying the oppression is as horrible as being shot in the street for having "too much melanin." I'm saying skinny people can fit on seats in cars, and public transportation. Skinny people are not less likely to be believed and taken seriously by doctors when they need medical attention for cancer just because they're skinny. Generally, skinny people don't need custom clothes that help them look good and feel good that fit them.
I need to clarify that I'm not saying it never happens when someone shames someone for being so thin you can see their bones. But notice how I have to specify that they need to be skeletal thin for me to say this properly. Skinny as an adjective is a spectrum just like fat. But only few are shamed on the spectrum of skinny, while everyone on the spectrum of fat are shamed.
Thanks for coming to my Ted Talk.
If you have had any level of body shaming, I'm truly sorry to you. I understand the struggle and I know it's hard. Don't forget to eat, drink water, slow down, and take time to yourself.