Have a look at the typical module schematic from here (the equation for the excitation voltage is obviously incorrect):
And the Avia chip datasheet from here.
Digital supply current 0.1mA (typical)
Analog supply current 1.4mA (typical)
Regulator divider using 8.2k/20k divider - 1.25V/8.2kΩ = 0.15mA (typical)
Excitation voltage: 1.25V*(20kΩ+8.2kΩ)/8.2kΩ= 4.3V (typical)
Load cell current: 4.3V/350Ω = 11.9mA (typical)
Total: 13.55mA typical (active) with load cell connected
Total: 1.65mA typical (active) with load cell disconnected