Electronic – arduino – Problem of noise with load cell and INA125P + Arduino Uno

I am here with a problem that I cannot solve. Here are the facts:

I have a load cell : http://www.robotshop.com/en/micro-load-cell-50-kg.html
that I want to use in both directions, from -30kg to 30kg approximately (it will be a force sensor in some applications).

To obtain the signal coming from the load cell on my Arduino, I am using an INA125P.

Due to technical constraints, I need to use a 9V battery to power the whole system.
Also, needing to measure the force in both directions, I need the signal that comes out of the INA125P tp be referenced to 2.5V approximately.
Here is the actual schematic:

My problem:
When I am in certain locations, where probably there is a lot of parasitics, the signal from the INA125P varies about 5% when my hand is near the load cell, but not touching it! It only happens at some locations but not others. For example, at home, there is no problem; the signal is very stable. Also, the amplitude of the noise seems to be proportional to the gain of the amplifier.

What could be the problem ?

Thank you

UPDATE 6/05 : To be more precise about the variation, here are some examples:
– When the load cell lays on a table, no forces on it, the signal (after ADC) is 440 (the value are from 0 to 1024). If I approach my hand close to the cell without touching it, the signal drops to 425 and if I touch it, it drops a little bit more to approximately 400.
– When I have the load cell in my hand, and I lift my arm up of about 20 inches, the signal goes up to 460, when I come back to the table, the signal returns back to its initial value.

Therefore the signal is not oscillating, and the variations are always approximately the same, it is not aleatory.