As far as I can ascertain (having not yet accessed the full text), this study did not specifically examine maternal request caesareans, and in fact found that "after all factors were taken into account there was a stronger link with emergency caesarean than with pre-planned ones, although the numbers were small for this calculation."(1)
It is very concerning therefore that the authors appear to be presenting this study to the media as potential evidence to dissuade women from choosing a planned caesarean. For example, "A mother who chooses caesarean delivery on maternal request should be aware of [these] potential health risks... including childhood obesity."(1) And, "An association... would provide an important rationale to avoid non-medically indicated caesarean section".(2)
Hypothetical theories about the potential impact of gut bacteria remain unproven, and women choosing a caesarean are weighing up other perinatal risks such as stillbirth, asphxiation, shoulder dystocia and serious intrapartum injuries, as well as
The authors of Birth by Cesarean Delivery and Failure on First Otoacoustic Emissions Hearing Test (Tatiana Smolkin et al) evaluated 1,653 babies born at 35 weeks' or more gestation, and found that those born via c-section (CD) "had significantly higher failure rates" when their hearing was first tested. They "speculate that CD is accompanied by retained fluid in middle ear which may impair neonatal hearing", and recommend that the timing of first otoacoustic emissions "should preferably be postponed beyond 48 hours of age to improve OAE passage and minimize maternal anxiety and costs." 
Two weeks following submission, my letter in response to the obesity study was published, June 6, in the BMJ Archives of Disease in Childhood. Titled, "Findings do not inform maternal request caesarean risk", it reads:
