Would I be correct in guessing you've been watching (or reading) Carl Sagan's Cosmos?

There's no reason to believe it was the butt of jokes in Democritus' time. At that time Abdera was a pretty important city, grand enough to host to Xerxes during his invasion well enough that Xerxes presented gifts to the city (remember most Greeks were on Xerxes' side). But the 5th century BCE was its peak.

Starting in the 1st century BCE we do start seeing remarks along the lines that Sagan talks about. Cicero, Letters to Atticus 4.17, uses it as a byword to describe a loud discussion in the senate, and Letters to Atticus 7.7, refers to a policy decision that makes no sense as 'Abderitic'.

Some further references in Martial and Juvenal (1st century CE) indicate that it had a reputation as a rustic backwater. Martial, Epigrams 10.25, writes

If you think [a guy who put his hand in a fire] is a badass, then you have the heart of the Abderan people.

Juvenal, Satires 10.50, talks about Democritus and describes Abdera as rustic, and calls it the 'land of sheep beneath a thick mist'. Translations typically convert these sentiments into slights about Abderan intelligence. That isn't strictly warranted by the Latin text. They look to me more like mockery of a rustic town with a grand past.

Those translations are motivated by later references: there are 18 jokes about stupid Abderans in a collection of jokes from late antiquity called Philogelos, or 'the laughter-lover'. We don't have too much more information than I've already presented, so we don't know exactly how that reputation evolved. There are a couple of anecdotes in Athenaeus and Galen, which add flavour, but still don't really tell us anything about how the reputation developed over time.

Here's a passage from a 2016 book chapter by Ranja Knöbl that goes through the available evidence, starting at the bottom of page 279 and carrying on to page 281. Depending on the context for this question, if I'm right that you came to this through Cosmos, the main point in response to that would be that the reputation is much later than Democritus.