Adam West was playing the role handed to him: making fun of what is honestly pretty ridiculous. Grown men in tights.
He had to have known that the television show was sarcasm at its best, and he played the character as such awesomely. Given the costume he had to wear, it’s really difficult to look like a bad-ass in those gray tights. Also, he didn’t even try to disguise his voice when he wasn’t Bruce Wayne. What would be the point?
Adam West was able to deliver subtle jokes and vague references to things that weren't on 60's television in his deadpan dry straightman overly-logical tone.
Look at examples:
“It’s obvious. Only a criminal would disguise himself as a licensed, bonded guard yet callously park in front of a fire hydrant.”
“Salt and corrosion. The infamous old enemies of the crime fighter”
Robin: “You can’t get away from Batman that easy!”
Batman: “Easily.”
Robin: “Easily.”
Batman: “Good grammar is essential, Robin.”
Robin: “Thank you.”
Batman: “You’re welcome.”
Robin: “Let’s go!”
Batman: “Not you, Robin. They have strict licensing laws in this country. A boy of your age is not allowed in a drinking tavern.”
“Robin: Where’d you get a live fish, Batman?”
Batman: “The true crimefighter always carries everything he needs in his utility belt, Robin.”
“It is the duty of every good citizen of Gotham City to report meeting a man from Mars in a public park”.
“Let that be a lesson. In future, be more careful from who you accept free lemonade.
Robin: "Boy! That was our closest call ever! I have to admit that I was pretty scared!"
Batman: "I wasn't scared in the least."
Robin: "Not at all?"
Batman: "Haven't you noticed how we always escape the vicious ensnarements of our enemies?"
Robin: "Yeah, because we're smarter than they are!"
Batman: "I like to think it's because our hearts are pure."
Robin, about Catwoman: "Do you think she'll kill Batgirl?"
Batman: "Or worse, Robin. Or worse."
