I think peers are a big influence on children and adolescents because they spend most of their days in school, where they are constantly interacting with them. The idea that social development is related to popularity is not that surprising to me. I think this might not even be necessarily a causal relationship, as much as a correlation. Children who are outgoing and get along with others are more likely to have many friends and be popular among their peers.
As far as the connection between physical and social development, it makes sense that they would develop at the same rate. For example, when a toddler is able to walk and talk, they can interact more with those around them. Also, when children are older, they start going to preschool and kindergarten. This gives them more opportunities to interact with others and develop their social skills, which they've only been able to develop at home so far.