HI Robbie,
I am actually confuse between your actual circuit and your test circuit.It seems that your actual circuit has a differential inputs while your test circuit is single ended at V+.
Are you familiar with the diamond plots(Common mode voltage vs Output voltage)? This is a very important plots which gives you the limits of your operation. This is one of the most common problems experienced by our customers and it is the main reason why we created this tool.
Let's focus on your actual circuit. Are you getting your input signal from a wheatstone bridge with an excitation voltage of 3.3 V? Does the inputs of the AD8237 are AC coupled? If yes, are you planning to apply bias on pin 2 and pin 3? What is the supply voltage of the AD8237? What is your expected differential input voltage ( Vin+ - Vin-)? Vref? Gain? I just want to make sure that I know exactly your setup for us to check if we are missing something. Uploading your schematic with expected voltage range on each nodes will also be very helpful.
Thanks and best regards,
Emman