Why did atticus unbutton his vest and loosen his collar?

I'm not sure if this is THE answer.

But clothes represent the restrictions society puts on people. People dress a certain way based on their station, on the occassion, etc.

So when Atticus loosens his clothing, he is loosening the binds of society and culture on himself.

The reason Atticus loosens his clothes is very simple, the jury is made up of farmers (they probley dont own suits) so to connect with them on a personal level and not seem condisending Atticus loosens and takes off his suit.