I don't think that the word duty is considered funny usually. Could it be that people were laughing because of the context in which it was used? Or maybe it was another word that sounded like it?
Duty is a word that is regularly used in business, law, education, etc., in a serious tone or in a business-like tone, or in any regular conversation with a regular tone. The very meaning of the word has a relatively serious connotation to it, as it is talking about what you must do.
(Unless you were watching shows that encourage rebellion against duty, then they may be laughing at the word.)