Laws in San Francisco aim to prevent fat discrimination
Attacking someone for being fat should be a hate crime, campaigners say.
They want so-called "fat-ism" to be made illegal on the same grounds as race, age and religious discrimination.
A demonstration was held outside the offices of the mayor of London asking him to lead the way in making sure employers are not prejudiced.
Protesters want the UK to follow San Francisco, where a law bans "fat-ism" in housing and employment and stops doctors pressing patients to slim down.
Sondra Solway, a San Francisco lawyer, said: "The San Francisco ordinance says you may want to mention weight to the patient but if the patient says they do not want to talk about that then you are asked to respect those wishes."
In the UK, size is not a protected characteristic under discrimination legislation.
The campaigners, who belong to the Size Acceptance Movement, say surveys show 93% of employers would rather employ a thin person than a fat one even if they are equally qualified.
Kathryn Szrodecki, who campaigns on behalf of overweight people, said that in the UK fat people were stared at, pointed at, talked about and attacked.
She said: "I have been discriminated against - I am a YMCA qualified fitness instructor, but I have gone for jobs and been laughed off the premises."
Another campaigner, Marsha Coupe, said: "I have been punched, I have had beer thrown in my face, I have had people attack me on the train.
"They say 'Move out of the way fatty! Well person coming down the aisle!'"
Ms Szrodecki said: "This is a very common event - someone being beaten up should be a crime.
"It is not about who you are or what you have done, it is just about the way you look.
"You are allowed to shame us just because of the way we look."
Dr Ian Campbell of the charity Weight Concern said he was doubtful that legislation would have any immediate effect on the situation.
He said: "People who are very overweight do experience a lot of prejudice both in their social life and working life and do need some protection.
"We know that genetic and social reasons can lead to this very complex problem.
"For instance, people in inner cities are much more likely to be overweight because of poorer education, poorer housing and poorer job opportunities.
"Not everyone has a free choice about controlling their weight."
A spokesman for the Equality and Human Rights Commission said size was already protected by the legislation if it was caused by a disability: "Potentially human rights legislation would also cover people by protecting their right to work."
A full report appears in Inside Out London Tonight at 1930 BST on BBC1.