I want a better suppy for my AD620 that allows the output to fully swing between 0-5 V, using my 8 V Lilon battery.

I think I can manage this by setting the virtual ground at +2.5 V. The resistors needed would be a ratio of 22:10 or 33:15 so for example 22k and 10k.

Simulating in LTSpice wi th 'operating point (.op)' shows VGND at 2.5 V. To the breadboard!

The 10k's on the right are for testing; whatever the values of those resistors, the output of the opamp should not change.

Measurements

Vcc = 8.19 V

Without the right two resistors, VGND = 2.55 V

With 10k-10k voltage divider on the output, VGND = 2.55 V

With 10k-1k voltage divider on the output, VGND = 2.55 V

With 1k-10k voltage divider on the output, VGND = 2.70 V

Then instead of the two resistors I placed a 100k potentiometer. When at 100k - 0k the output stays the same. Only when the top resistance goes down to about 1k the balance is off and the output quickly goes to Vcc.