It is true that gold is diamagnetic and tungsten is paramagnetic.
The "magnetic susceptibility" of the materials is needed to quantify the effect.
Here is a table of magnetic susceptibilities:
http://www-d0.fnal.gov/hardware/cal/lvps_info/engineering/elementmagn.pdf
The problem I see with this technique is, as you can see by looking at the values in the table, that there are substances having susceptibilities hundreds or even thousands of times the absolute value of susceptibilities of gold and tungsten, not to mention ferromagnetic materials. In other words, a small impurity in the gold could give the same result as the entire bar being tungsten. The bar could be 99.9% pure gold and give the same result as 100% tungsten depending upon the other 0.1%.
Also, keep in mind that when tungsten faking has actually occurred, the gold bar has been drilled out and only a percentage of the gold bar has been replaced by tungsten. If, say 30% of the gold is replaced by tungsten, you will not observe a net attractive force on the bar, considering the weighted average of the opposite-sign susceptibilities of gold and tungsten.
There are two other important issues with the technique. Firstly, oxygen is paramagnetic. As you can seen in the table, oxygen has a much greater molar magnetic susceptibility than tungsten. When the gold bar is placed above the balance, air containing paramagnetic oxygen is displaced. This effect must be considered. Second, the magnetic susceptibility of the plastic envelope must be considered.
Also, the gradient of the magnetic field (how the field's intensity varies with space) determines the force, rather than the strength of the magnetic field. Magnetic susceptibility experiments are often part of undergraduate physical chemistry lab course. Typically, the sample is suspended from a microgram balance, the sample being between the poles of a large electromagnetic.
Checking for ultrasound echos coming from the interior of the bar at a gold/tungsten interface and measuring the speed of sound in the bar are techniques in use to rule out gold plated tungsten bars.