Funtestiq!  Numbers

Answer: One.

The agent needs to weigh only one single time if he does the following:  

He takes one coin from the first stack, takes two from the second stack,  three from the third, four from the fourth, and so on, till he's done with all 10 stacks.  He then weighs the 45 coins thus collected together and observes by how many grams the weighing result excels what 45 good coins would have yielded.   If, for instance, he gets a reading of 48, the 3rd stack of coins must be counterfeit.