Load cell, INA125P AnalogReference, signal stability

I am trying to improve reading from load cell (body scale) attached to arduino nano. I use INA125P exactly like the following wiring but with 100ohm resistor:

When nano is powered by 9v battery readings from A0 pin are very stable. When nano is powered by 9v adapter or usb readings from A0 variate form 430 to 410.

I noticed that when i touch with hand Aref pin wire, the readings get stable just like when powering nano with battery. Why is that?
How can i use Aref pin to achieve same result as with battery power?

I tried to use INA125P 5v on pin 15 as Aref for nano and load cell power but still unstable readings.

Next step is to use capacitors but i wonder why after touching the Aref pin wire on nano the readings get stable when on usb power?

Thanks for any help.

The input circuitry to the Arduino is probably picking up 50/60Hz hum from the household wiring. This suggests that the circuitry is not properly enclosed and grounded (which you can accomplish by touching with your hand).

Thank you,
Now i change little wiring:
Nano is powered on VIN pin by 9v from adapter, INA is powered from VIN pin of nano 9v, Load cell is powered from pins 4 and 15 of INA (Vref5v and Vrefout pins).
Aref pin of nano is connected to 15 pin of INA (Vref5v) and in code i set analog referense to external.

In that configuration results are the same: on 9v battery power very stable results (425 reading from analog0 with zero load and not changing); on 9v from adapter results are unstable (419 to 430 reading from analog0 with zero load).

Experimenting now with capacitors - put 100uF between 9v an ground, 10nf between S+, S- of load cell and INA inputs. Result still the same.
Can't make adapter powering to work as battery powering.
Any help will be good. Thanks.

Finally solved my issue from a sentence in another forum:

The INA ground and the Arduino ground need to be separate and meet at a single point where power comes to the circuit.

The ground was the problem, i separated nano and ina grounds, leave the capacitors but added another one 220uf where two grounds are meeting. In that meeting point plugs 220uf capacitor and 9v from nano vin pin.