1) You cant say that unilaterally - Fat shaming may very well also prevent skinny people from becoming fat. You can't just look at already fat people.
2) These self reported "weight discrimination" studies have so many biases you really shouldn't take them as fact.
3) The usual correlation =/= causation speech. It could very well be that amount of discrimination also varies with weight (duh) and that those that get a lot of discrimination are already past the point of motivation to change (just one of many alternative theories. This specific example isn't the best by any stretch).
All in all, it just does not make as much intuitive sense that fat jokes (among other things) encourage people to stay fat and this little study is definitely not enough to override occams razor in my opinion.
Did you bother to read the abstract of the source provided? It directly refutes pretty much all of your points including a control group. For your convenience, I've italicized the relevant text:
>Participants were drawn from the Health and Retirement Study, a nationally representative longitudinal survey of community-dwelling US residents. A total of 6,157 participants (58.6% female) completed the discrimination measure and had weight and height available from the 2006 and 2010 assessments. Participants who experienced weight discrimination were approximately 2.5 times more likely to become obese by follow-up (OR = 2.54, 95% CI = 1.58–4.08) and participants who were obese at baseline were three times more likely to remain obese at follow up (OR = 3.20, 95% CI = 2.06–4.97) than those who had not experienced such discrimination. These effects held when controlling for demographic factors (age, sex, ethnicity, education) and when baseline BMI was included as a covariate.
All in all, it just does not make as much intuitive sense that fat jokes (among other things) encourage people to stay fat and this little study is definitely not enough to override occams razor in my opinion.