Your perspective on the way that obesity, and obesity research, interacts with health disparities research is important. As I am sure you know, Tracy Weitz did interesting work looking at bias in contraceptive counseling by weight status, and I think you are right that this could interact with other forms of bias. Finding ways to incorporate this perspective into your research, and eventual interventions, including bringing diverse patient stakeholders to the table, would be valuable.
And yes - I think the social communication piece of the barbershop intervention is particularly relevant to reproductive health, especially given what we know about fears of coercion and general mistrust of family planning providers.