Can you post some statistics on how exactly the number 200 was chosen, how does it perform, a graph that shows how many pageviews/revenues come from users with rep X ?
It was chosen using a scientific process similar to this (all characters are figments of Atwood's imagination):
Evil Jeff: We need advertising to keep our four-chambered stomach full, Jeff.
Jeff: It's a necessary evil, I know.
Good Jeff: So let's reduce advertising for common users.
Evil Jeff: Noooo!
Good Jeff: The idea that advertisements might be reduced later will encourage participation through selfish idealism! Evil Jeff, you must agree that it will work.
Evil Jeff: I suppose. At what point should advertisements be reduced?
Interruption Duck: Quack
Jeff: How about 200 reputation points?
Good Jeff: Sounds good.
Evil Jeff: I'm late for an appointment with Dogbert.
Long story short, it's a number someone pulled out of his unicorn.
I'm pretty sure it's an arbitrary number without any scientific basis as Welbog points out, but it turns out to be a good number. By far, the majority of StackOverflow users are one time users who don't even have an account and are dragged here via Google and we want to have maximum advertisement on those users without sacrificing user experience for StackOverflow contributors.
The threshold is meant to distinguish SO "users" from "one timers" and it's pretty successful at doing that: only ~25k of registered accounts (about 20 percent of them) have 200 reputation which means the threshold is not low. It's pretty easy to get 200 rep in a day or two -- this means it's not too high.
It has been said some times that the largest group of visitors are non-users through Google.
Of course, this is nothing else than yet another appearance of the Pareto principle (the 20-80 relation for the friends). If this holds true, then the bulk of the traffic comes from non-users that visit the site, that might have a greater chance of clicking on the ads, as they haven't seen the same ad over and over again. Also, you generate goodwill from users that drive the content, that generates the non-user traffic. It's a win win.
Considering that there are now 183849 registered users (so we are not counting unregistered visitors, that are in the number of a million), and there are only 21423 users with >= 200 rep points, there is 8.5 times more people looking at the "extended" advertising than the "reduced" advertising.