I mixed up who's asking what. Lefty, did you mean millivolt per Newton or Pound per excitation voltage?
Passive devices like strain gauges that are internally wired like the classic resistance Wheatstone bridge typically have a full scale output voltage of some small millivolt output voltage, however the specific output voltage is dependent on what voltage you supply to excite the bridge, 10vdc, 5vdc, 2.5vdc, etc.
As bridge excitation voltage value is a user choice, how should a strain gauge manufacture state the full scale millivolt output for their device not knowing what voltage you will excite the bridge at? Rather then to list a number of standard output voltages Vs Bridge excitation voltage, they just rate it like this: 10mv/V. That's not division, it says it will develop 10mv per volt of bridge excitation voltage.
That means if your drive the bridge with one volt and load the cell to it's maximum rated strain it will develop 10mv output, and you can scale it to any voltage you want to actually use, so at 5vdc bridge drive will have a full scale output voltage of 50mv.
This is not the same spec as what amount force is required (in grams, ounces, tons, etc) to reach 100% full scale output, that is a separate specification independent of the bridge electrical sensitivity specification of xx mV/V.