LM7805 outputting ~2.5v

Yes, this is possible. See this AVR-as-RFID project for an example, which explains:

The coil actually powers the AVR through two of its I/O pins. Nearly every chip out there has clamping diodes on its I/O pins, which prevent voltages on that pin from rising above the chip’s supply voltage or sinking below ground. These diodes are useful for arresting static discharge.When you first hold the RFID tag up to a reader, the chip has no power- the supply voltage is zero. When the coil starts to pick up power from the RFID reader, these two I/O pins are presented with a sine wave, a few volts in amplitude. Anywhere that sine wave exceeds the supply voltage, some energy is diverted from the coil to the chip’s supply rails, via the clamping diode. The end result is that the chip is powered, and the coil’s sine wave is truncated. The top and bottom of the sine have been chopped off, and it looks a lot more like a square wave now.

So the clamping diodes, intended to protect your AVR from overvoltage, are conducting current from the input pin to the supply rail, powering the rest of the AVR.

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.