If I use Croagunk's "Poison Up" to attack the same Defending Pokemon on successive turns, does the amount of damage counters due to Poison increase? For example, the first time I use it the poisoned Defending Pokemon starts taking 3 more damage counters between turns, then if I use it again it starts taking 6 more damage counters (3+3), then 9 more damage counters (3+3+3), and so on?
Yes, each time you use Poison Up it increases the amount of poison damage by "3 more" than what the Defending Pokemon was already taking at the time of the attack.
Poison Up