No, because it's a triggered ability that only triggers once when you cast a spell. If you control multiple permanents with extort though, each one triggers separately and you can use it that many times.

Does extort stack?

EDIT: Clarifying - you'll have to pay for each trigger, since they are treated as separate objects by the ability. If it said "If you do, each opponent loses 1 life per each permanent with Extort you control" then the life-loss would stack.

Do you have to pay for each instance of extort?

You're right that Extort costs {W/B} for each creature: each instance of Extort is a separate triggered ability. Each one triggers, and then your friend may pay for the first, for the second, and so on.