Let's say there is a situation where you predict your opponent will switch out, so you switch into a Pokemon with stakeout and they send out their Pokemon. Would the Pokemon that was sent out take double damage from stakeout?
Stakeout doubles the power of moves used against targets that have switched in this turn.
It won't double the power of the move because the the target didn't switch in that turn. If they switched in again, then it would do double damage. Source: https://bulbapedia.bulbagarden.net/wiki/Stakeout_(Ability)