I think there is an element of truth to your statement, a sense of insecurity on your behalf, and a lot to be said about how you present when being around people.
I ballooned in my weight over a couple of years due to a medication I was on - and yes, I absolutely got the look up , look down, look away thing from the skinny mum brigade and randoms in the street. A friend calls it the "Hi I'm beautiful and nope, you're not" look. It was upsetting, I get you but I got myself over it.
I have since lost close to 20kg by dumping that medication and yes, I seem to be approached more often and looked at differently. My position on this, which is pretty set in stone, is that those individuals are shallow and not worth bothering with anyway. I'm still the same person, my looks should not matter.
Having said that - what is appropriate clothing that covers you up? Baggy clothing ( I found) is almost like you're are apologising for your size, which you shouldn't, and makes your weight more obvious because you are trying to hide it. I have a friend who is a size 22 and she rocks dramatic kaftans , leggings and biker boots with big earrings and beautifully styled hair. Plus she gives no fucks at all. She is one of the most socially sought after people I know. It's very much down to her attitude.
You may find you are projecting your fears of rejection with your body language without realising it as a PP said, and the clothing maybe contributing to that. Avoid high street styles and current fashions, and find a "look" that makes you feel good.
Lastly, have no expectations that you will form relationships at the school gate. Do your own thing, and focus on your child. These are parents of your children's potential friends - not friends for you. I actively avoid becoming friends with school parents, or going to "drinks with the girls"from school as I believe it's not appropriate and groups of women are my idea of hell. ( But that is just me).
And to wrap it up, if you can start on a sensible healthy eating plan, and some moderate exercise you'll be doing yourself a favour. Even if you don't loose shedloads of weight immediately it will start you feeling better within yourself and make you want to beat yourself up less.

And as for why? I'd put it down to some people being superficial asshats.