To cut the technical stuff, our intestines support "good" microbes - bacteria that helps keep us healthy in a symbiotic relationship. When those good microbes are decimated, "bad" microbes flourish, causing a whole lot of problems - even vision difficulties. You name it - if it is screwing up your health, there's a fair chance it is because of a shortage of good microbes. And the things that cause obesity can be triggered, as well.
There are several things that can decimate the population of good flora in the gut, but the biggest offender is antibiotics. Doctors prescibe antibiotics indiscriminately, but never get around to telling you that once your prescription is used up, you really need to replenish the good flora - antibiotics kill ALL the bacteria - the good and the bad. After a regimen of antibiotics, you should always pop probiotics for several days. Or, down a bunch of live culture yogurt for a week or two.
But that is not the only problem. Many of today's meat animals are fed antibiotics to keep them healthy in cramped conditions. The meat is infused with antibiotics, so unless you only eat naturally raised grass fed meat, you still need to boost the good flora regularly.
I'm not saying that probiotics will prevent obesity caused by over eating or eating bad choices. But there is evidence it will help prevent any obesity caused by contagion.
In choosing a probiotic, understand that stomach acids will kill most of the good flora before it can get to the gut, so you need to take them regularly. But the ones that do survive will multiply and populate your intestines.