Can I pay some of the cost of an activated ability lots of times to get more out of the effect?
You can sacrifice one and only one goblin. MTG cards are very specific in their language: it says "a goblin", so you can sacrifice a goblin, not two goblins, not three goblins. If the card was designed to let you sacrifice multiple goblins, it would say


  {T}, sacrifice any number of goblins: Tar Pitcher deals 2 damage to any target for each goblin sacrificed. You may choose different targets for each one.


(it would also be overpowered given the ease of creating goblin tokens)