Why did Little Bill kick the Englishman's Butt?

Simple. Little Bill knew the ho's put the word out that they were going to pay a thousand dollars for two assassinations, so he was on the lookout for any strangers that came into town, specifically those carrying firearms.

So when English Bob shows up, Bill knows it's for the killing so he kicks his ass royally (had to say that) as a lesson to not only him, but anyone else who might be thinking of collecting the whore's gold. In today's world, sheriffs can't legally assault someone on suspicion, but things were different then, and Bill knew that the news of his assault on Bob would also get out.

So while it seemed he was minding his own business, his true business was to kill those two cowboys and collect the money.

Is very bad to steal Jobu's rum. Is very bad.

You missed a good movie. First of all, he was not "minding his own business" he was there to kill people and Bill knew it. Second, he was trying to pick a fight, going around insulting every American in town, on the way into town, etc. He deserved a good ass beating just for that! But as the other poster said, the real reason was to send a message. Very obvious.

I would say my memory is not what it used to be. But I don't remember what my memory used to be.

He didn't kick his butt. He sent a message to all the other guys who might be coming after the bounty.

The madam kinda explained this part. As soon as Englishman Bob left, she said, "Now nobody's gonna' come, after they see what happened to Bob."

Bill beat up Englishman Bob to make a statement for anyone coming into town for the bounty; he wanted to make people too afraid to try for the bounty.

Bill was a good lawman. He wanted to save lives and protect the peace.