First, as to your calibration and achieving 1.0 PSIG.
Give this article a read as it is based on an Arduino but would work with any pressure sensor. While the article focuses on measuring level in a tank if the level is known the pressure can be calculated. I place a tube within a larger diameter tube and place a cap on the larger tube and fill it with water. If I insert my small diameter tube into the water and down, then blow into the small tube as I push water out of the tube using air pressure the required pressure to get bubbles to escape the bottom of the tube is proportional to the the water level in the tube. If I take a large diameter PVC pipe and cap one end, my pipe is 36" tall (3 foot section of pipe) and place a ruler in it or beside it (clear pipe) then fill it to 27.68" of water (26.7" is close enough) you can figure when my narrow tube bubbles I am applying 1.0 PSIG. Short of an elaborate calibration system that will get you an accurate 1.0 PSIG or less with less water level. 6.9" water = 0.250 PSIG, 13.8" water = 0.5 PSIG, 20.8" water = 0.750 PSIG and 27.7" water = 1.0 PSIG.
That said and as Carl points out, when you start using lower excitation voltages you gain needs increased and your accuracy suffers. This is not a good practice. Also, you want the reference voltage to be as stable as possible. Any drift in the excitation voltage will reflect in the mV/V output of the bridge and then be amplified by the instrumentation amplifier. This is where it is wise and good practice to use a
stable 10 volt reference for the bridge excitation. A Google of 10 Volt Reference will bring up a dozen hits similar to the link. If you want to accurately measure and resolve 1.0 PSIG you really want good stability.
As to the Reference terminal:
REFERENCE TERMINAL
The reference terminal potential defines the zero output voltage
and is especially useful when the load does not share a precise
ground with the rest of the system. It provides a direct means of
injecting a precise offset to the output, with an allowable range
of 2 V within the supply voltages. Parasitic resistance should be
kept to a minimum for optimum CMR.
For your application reference gets tied to ground. See the AD620 data sheet. Also the +VS (Positive Vsupply) and -VS 9Negative Vsupply) are your power for the instrumentation amplifier. I do not understand the reference to a Function Generator?
This is the data sheet for the AD620, have you read it and looked at the examples? Pin 6 the output would go to your uC (Arduino Analog Input).
Ron