We've known for a while that it definitely plays some role, but almost all of the experiments done so far have been done on mice, not humans.
This month, a study conducted at Lund University in Sweden on 674 subjects found that probiotic health definitely plays a role. Subjects who had higher levels of obesity related metabolites also exhibited an overgrowth in four specific kinds of unfriendly bacteria.
What this suggests is that the gut microbiome could be a mediator between high levels of these metabolites and obesity.
The moral of the story is this: if you want to burn fat and be healthy, one of the first steps you need to take is in fixing your digestion and providing a good environment in your intestinal tract for friendly bacterial growth.