My personal Scale project has a huge drift in its readings for weight

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it's great that you suggested so many scenarios for the cause of my problem, but I need more clarification from your part.

1-what is the base resistance?
2-what is casing the load cell to warm up and how to check for that ?

- 0v and power leads should all be star connected to a single point 

I didn't grasp how to connect power and 5v to a single point.

  1. The resistance of the load cell in ohms with no weight it .
  2. If the resistance is outside of its spec or it’s wired wrong then the current may warm it up causing a drift in the measured value . Maybe the supplied display switches the load cell on for a short period then off for a longer period to avoid that ? Investigate with a voltmeter
    All you 0v connections from each device should terminate at a point close to the Ov power supply and not looped device to device .

If you stand on the scale for a long time, do your feet warm it up ?

Thank you for your informative response,
no I don't feel any warm when standing on the scale.

I think there is an issue with my wiring, as the project has LCD screen with I2C, HX711, and an ultrasonic module, and all of them have ground and 5v pins.
I chose to connect a single wire from the Arduino Nano ground pin and at the end of the wire I connected 3 pins and I connected each pin the the ground pin of each component.
so I think it resembles your first drawing.
That may cause the the drift in the scale reading, and Also it may causing some bizarre behavior of the LCD screen as it sometimes some letters disappear and some times the connection to the serial monitor is lost.
I will do some more investigations and I will give you feedback

Here is a photo of my board and its wiring.


as you can see the pins adjacent to the HX711 are has 2 collections the first collection has 3 pins connected directly to the ground pin of the Arduino nano, the other collection has 3 pins connected directly to the 5v pin of the Arduino Nano .
I tried disconnecting the ground and 5 volt of the screen and the the ultrasonic sensor but all the sudden the sketch stopped working all together , So what you suggest?

I suggest going back to the beginning. Set aside your nice box. Use just a Nano and an HX711.

If that still gives the large drift, then you have fewer variables to study.

BTW, the "load call amp" typo on the HX711 does not inspire confidence. I'd use one from a reputable supplier, such as SparkFun.