Here's a major challenge for the Cult of Gravity:
http://www.wired.com/wiredscience/2013/09/high-gravitational-constant/
For 200 years, they've been trying to figure out how to measure something that doesn't exist.
Not really. The fact that G has been measured for 200 years and comes to within 240 parts per million (that's 0.024% error) implies there
is something going on, but we just don't know the exact value of it.
Think of pi. When Zu Chongzhi calculated pi to be 3.141592920, later calculations showed he was off by 2.664 * 10
-7. Not much, but, in the words of your article, "a constant should be constant." If pi was a real constant, why does its value change?
For something like gravity, which isn't just calculation but experimenting to try and find a very, very weak force, having difficulties in narrowing it down to an exact number is to be expected. At that scale a person standing near the experiment can severely alter the results.
Just as our methods of calculating pi have become more exact over time, so will our methods of calculating G. But we're still transitioning from the Zu Chongzhi to Christoph Grienberger.