Voltage range of a differential pressure sensor px26, and opamp saturation
What you have to remember about the AD620 (and other instumentation amps and most opamps) is that their inputs only work correctly when the voltages applied to them are within a limited range. This limited range is governed by the power rails.

For instance, the AD620 data sheet says: -

Input Voltage Range = -Vs+1.9 volts to +Vs-1.2 volts


This means, that for a +/-5V supply, the valid input voltage range is: -

-3.1 volts to +3.8 volts. 


For a 0 to 10V supply it is: -

+1.9 volts to 8.8 volts.


Whatever you do, make sure you don't get too close to these limits or you'll get disappointing results. Next is the output voltage swing. The data sheet says this: -

Output voltage range = -Vs+1.1 volts to +Vs-1.2 volts


For a 0 to 10V supply this means the output can fall as low as +1.1 volts and rise as high as 3.8 volts.

If you can get your sensor to input the right voltage range that's a start. Next, use the REF pin to bias the output so that it remains within the output limits imposed above and finally, try using a potential divider to reduce the output range that that suitable for your arduino.

One last bit of advice - read the data sheet and keep asking questions if there is something you don't understand in the data sheet. A lot of the more experienced guys on this site will tell you that the data sheet is all you have - no belief system involved except to believe the manufacturers have told the truth - invariably they have of course.