I don't know the nuance of "then". I think it is not necessary here.
Native speaker’s answer
Rebecca
The word "then" in this case means "afterwards" or "later". It is necessary in this sentence because it tells the time at which something happens, expressing that people are more likely to agree to a bigger request after or once they have already agreed to a smaller request. Here's a few examples of "then" in similar contexts: Ex: I'm going to go to the store and then I'll come home. Ex: Let's get food and then go to the movies.