Well if one of the bodies is the entire earth, then the force of attraction between the earth and a smaller object is called the object's weight, and is measured by an ordinary scales.
If you want to measure the force of attraction between two small bodies (small compared to the earth, let's say two apples or two battleships) then the problem is much, much harder.
The reason is that gravity is an exceedingly
weak force in relation to the other known force-generating interactions between particles. For example, a proton and an electron are attracted to each other by virtue their electromagnetic attraction (opposite electrical charge) and gravitation (both have mass). But the former exceeds the latter by something like 40 powers of 10!
So any apparatus for measuring gravitation must be cleverly designed with fastidious attention to detail.
A famous series of experiments by
Eötvös at the start of the 20th C used an exquisitely sensitive torsion apparatus consisting of two masses on either end of a rod, hung from a thin fiber. He confirmed that inertial mass and gravitational mass were proportional to better than one part in 10
8.
Modern improvements have pushed the accuracy to better than one part in 10
12, according to the same article cited. Perhaps future observations in a space-based lab will improve on this further.
Great question!
