The mechanism is recognition. A payoff works because the audience remembers the setup, and remembering it is itself a small pleasure that gets attributed to the story rather than to their own memory. This is why payoffs are the cheapest emotional effect available and why over-using them makes a piece feel mechanical.
The ratio matters. Every setup you introduce is a debt, and unpaid debts accumulate as a vague sense that the piece did not add up. It is better to have three setups all paid than nine of which five land. Cutting an unpaid setup is almost always an improvement.
The strongest version reverses the meaning rather than repeating it. A line that was a joke in the first minute and is not a joke in the last minute is doing far more than a line that simply recurs.
What is setup and payoff?
Establishing something early and returning to it later with new weight. It produces the sense that an ending was earned, because the audience recognises the element and attributes the satisfaction to the story.
How many setups should a short film have?
Few, and all of them paid. Three paid setups beat nine of which five land, because unpaid setups accumulate into a general feeling that the piece did not add up.