How did 舆论 come to represent Public Opinion?
Interesting question! 

When I was a student, I was wondering why until I read a 词(Cí, a type of poery) by famous writer 辛弃疾(I really like reading his works). In that Ci, I read a sentence "百炼都成绕指，万事直须称好，人世几舆台", I got stuck with the word "舆台". The note said, "舆台“ meant "people at a lower rank". In ancient times, people were classified into 10 classes. The sixth class is 舆 and the tenth class is 台. So where does this word come from?

In the famous historical book 《左传》, in its section 《昭公七年》, it records a talk between two men, one says, 


  天有十日，人有十等，下所以事上，上所以共神也。故王臣公，公臣大夫，大夫臣士，士臣皂，皂臣舆，舆臣隶，隶臣僚，僚臣仆，仆臣台，马有圉，牛有牧，以待百事。


This text shows the 10 classes are: 王(king), 公(duke),大夫，士，皂,舆,隶,僚,仆,台. 

So 舆 could mean people who is at a lower rank, a member of grass-root. That's why “舆论" means “public opinion".