By the way, if you use the HX711, then you'll be able to read most of the load cell's range, but not all of it.
To get the widest range, your sketch will need to use HX711 Channel B (whereas most example sketches use Channel A).
With the approximately 4.3 v excitation from the HX711 (E+ to E-), your 20 mV/V load cell will output about 86 mV at full load, whereas Channel B clips at about 67 mV. (Channel A clips at 17 mV or 34 mV, depending on the gain setting, so if you're only using a third or less of the load cell capacity, you could use Channel A.)
One advantage of the HX711 over the ADS1116 is that it (the HX711) has an stable in-built excitation source for the load cell, so the ADC output is not sensitive to power supply voltage changes (it's "ratiometric"). The ADS has a stable reference voltage, but that voltage can't be used to excite the load cell; to avoid errors due to excitation voltage fluctuations, the load cell needs a very stable excitation source (something other than from USB or wall wart).