One needs to read Shakespeare in an annotated edition that explains the archaic words and sayings. Here is an annotation I found for the capon verse: “And then the justice, In fair round belly with good capon lined,” [good capon lined]: a lined pocket of a coat, meaning one bribed with the present of a fat chicken (a capon is a cockerel that has been castrated or neutered). In Shakespeare's day it was a common complaint that those who wished for justice from county magistrates had to bring presents with them. Such magistrates were known as basket justices.