Electrical – Load cell amplifier inverse voltage output

It looks like you have a bipolar differential input signal, but your output can only be unipolar because the REF pin is tied to -VS. If your input is AC, your output would be clipped at zero, so you're measuring it as half what you expect. Try moving REF up to 5V maybe.

If the scales are AC powered, the 0V in the scales maybe connected back to the AC earth and you are experiencing some problems there. Alternatively, when you measure the 5V on the scales, you might be connecting to -5V and 0V and convincing yourself it is +5V and 0V - this will work fine when the arduino powers it but give nonesense when you use the power from the scales.

What you should do is connect a common ground (0V) between the scales and the arduino and measure what the voltages on the scale are again. If they read negative values or are not how you expected them to be there is likely a mismatch in power supplies. Check also that you still measure about 2.5V on the midpoints.

It's a bit hit-and-miss doing stuff like this and you may get different values but if they are different to what you expect (with the common 0V) then there is a mismatch.

Another possibility is how the scales (when connected to loadcell) do their measurement. You can't rule out that they are doing an AC measurment with dc superimposed - you measure 5V but in fact there maybe a significant AC signal (probabaly between 100Hz and 10kHz) superimposed that your meter is oblivious to.