Programming an almost linear graph

Yes. All in Excel. It's not SAS, but I have it handy. I've done a bit of fiddling with your data and I have a couple of observations.
(1) I think your last data point [4.620,19035] is bogus
(2) I think that the underlying volts/gram relationship is linear to well within the accuracy of the measurements you've made, and
(3) I think that the source of the errors is A/D sampling error, specifically in the imperfect values in the A/D's resistance ladder.

The orange sawtooth series is the difference between the linear regression and the actual gram values. I bet you a buck, that the saw tooths correlate with the switching of specific bits of the A/D value and that would be an indication of error in the resistor ladder network used by the A/D sampler.

The error curve does not have any simple shape that would indicate a correctable non-linearity in the volt/gram function.