It's not really that simple.
There are plenty of larger women who are very popular in their social circles, very successful in their professional careers and don't have any issues in their romantic lives. They'll usually have a ton of innate confidence and probably one or two of society's other privileges, like wealth. So it's not a strict rule by any means.
But obviously yes, the more societal privileges you have the better you're treated in general. Weight is far from the only example. The reason for this is that a lot of people are shallow twats.
This is a real issue if you're talking about your professional life. But in your personal life, it's your responsibility to surround yourself with good people who aren't twats. I'm not fat, but if anyone I knew indicated that they'd treat someone differently based on their weight (or race, or sexuality, or height, or whatever) then I simply wouldn't have them in my friendship circle. Result? I have a social circle which contains people of all weights and no one is judged or made to feel uncomfortable, because no one else cares.
It is possible to find social circles where no one treats you differently if you're thin. I recommend it.
Personally, I know full well that I'd have been treated differently in many situations if I was white. But it's a pointless thought experiment dwelling on it. In all those instances where I was treated worse, I ask myself why it matters. Anyone who treats me worse because of my race is contemptible to me. I don't crave their approval, so I don't actually care how they treat me. I simply remove them from my life.