Using AD620 with load cell

You don't need a dual supply, but you'll need more design work than you seem aware of. You can use the AD620 with a single 5 volt supply since the load cell outputs ought to be about 2.5 volts and are within input limits. Set the reference to 1.1 volts. The ouput will then be restricted (according to the data sheet - and you DO have a copy of the data sheet and you HAVE tried to understand it, right?) to the range 1.1 to 3.7 volts. If you're willing to deal with 200 gram resolution you can stop right there.

If not, you need a second amplifier / offset generator. But first you would set the AD620 reference to something useful like 1.5 volts using a pair of resistors, and the gain for a 2 volt swing. Then, using a rail-to-rail op amp you would make a gain of 2.5 difference amplifier, and add in a 1.5 volt offset. The result would be (nominally) a 0 to 5 volt output. And before you ask - no, I won't give you a design. Do some research first. Google "differential amplifier" and actually try to understand what you read. Make a preliminary design and mess around with it. If you can't get it to work, describe your problem in detail on another question. Folks, including me, are glad to help - but I'm not going to do your work for you.

There is another consideration. First, you want to set your zero point at very slightly above zero volts. You should be able to check your data at zero load and see a little bit of noise. If the output of the amplifier is dead zero you know that your zero load level is less than 0 volts, but you don't know how much less. You can always subtract out a known zero offset, but there is no way to recover a completely unknown quantity. Losing a little bit of dynamic range or resolution is much less of a problem than not knowing what your zero point is.

In an ideal in amp the equation you have is true. In a real in amp we have to deal with something called offset voltage. This will be the real difference between the inverting and non-inverting inputs, as opposed to the 0 found in an ideal in amp.

Looking at the datasheet we see that it has a worst case value of 125uV. Multiplying this by the gain of 381 gives us about 48mV. Your output is therefore completely within spec.