Tweeting is an act performed in a social media. The question of a tweet being required to be silly or informative would depend on two factors, who is sending out the tweet and what is the reason of the tweet.
Say for example, you have a president sending out a tweet. Given that his position in the government, it is expected of him to be a symbol of credibility. It wouldn't be correct for him to spout senseless tweets. Even if it is a personal account assuming the position of a president has its expected conditions and persona to be maintained. On the other hand, if you are a comedian you are expected to cash in by also promoting your brand by sending out silly to funny tweets from time to time.
