It didn't affect my results, but I was very fit and healthy. I am unconvinced that obesity is necessarily the risk factor per se ("the mechanisms responsible for these outcomes are not well known nor understood" is more or less what I would say as well); it seems more likely that there is an underlying issue for both obesity and poor outcomes, such as fitness level. In fact, my GP said my pre-surgical test results showed that I was healthier than many skinny people he sees, and he wrote a letter stating that I was an excellent candidate for surgery.
Brassard does not have an explicit weight limit, nor is BMI a very good measure of obesity, so he was fine with the fact that I was significantly overweight but in great shape. Brassard also assured me that he could easily take weight into account the way he did swelling when it came to designing a good cosmetic outcome, and he appears to have been correct, as my results are excellent.
But, as other people have said, it likely depends on the person and their specific body, too.
