What was Big Willy Shakes going for?
Sir Hugh Evans is saying he doesn't want to be made fun of in front of everyone. So we think this is definitely about more than just his fight with Doctor Caius. Evans might be Welsh, but he's also the town clergyman and tutor. He doesn't want to be made a mockery all the time.
Apparently, "laughing-stock" was a common phrase in Shakespeare's day. It started from the idea of people being placed in the stocks in Medieval times. People were trapped in the stocks as punishment for a crime. Usually, it was in a public square or somewhere everyone could see them and mock their situation.
Sure, the stocks were uncomfortable, but the real punishment was the public humiliation of it all. Who would want to be seen by complete strangers, or their friends and neighbors in the stocks? It's not exactly a moment of crowning glory.
It wasn't really intended to be funny, but you can see how this saying developed over time. Someone was confined and restricted in a set area. The same way it is when someone is being humiliated.