Non-inverting amplifiers Offset Nulling
Although small, this opamp has some current flowing into it's inputs, about 300 nA. This causes a voltage drop across the resistor(s) that provide this input current. This opamp has a rail-to-rail input stage consisting of an NPN pair and a PNP pair. Since your input voltage is very low it will be only the PNP pair that does the actual work. So that means that a small current will flow OUT of the inputs ! This current wants to go to ground and it will mostly do so through R13. So 300 nA x 1 kohm = 0.3 mV intrinsic offset !

The positive input does not have any reistors so there will be no additional voltage drop. There's your offset ! You need to add a resistor in series with the + input of the opamp. Yes that goes against what you learned that opamps have zero input current ;-) If you make it a variable resistor you can calibrate out the offset.