Resistor Bridge sensors prove endlessly confusing because they require managing 2 signals. One is the mV signal and the other is knowing the excitation voltage Vex, applied across the bridge. If you measure these directly, as is done in the KL3356 (and all Beckhoff modules), you form a single value (mV/Vex) as the sensor's signal (s).
A calibration - either from the manufacturer, your Metrology Dept, or an in-place cal, determines the relation between lbf and the signal (s). Most people use a linear relation, which can be expressed as a single "span number" like "20.035 lbf/(mV/Vex)". It might also be expressed as "200.35 lbf/mV at 10 Vex". Note this is the inverse of "sensitivity". I usually fit a straight line with slope and offset (not forced thru zero), then ignore the offset since strain bridges require regular re-zeroing as the signal drifts (temperature). What you call "load cell sensitivity" is not really that. "2 mV/Vex" means that the full-scale signal is 2 mV for each 1 Vex, i.e. 20 mV max at 10 Vex. They would have to also tell you the load that give this, like "200.35 lbf".
An older method is to "shunt cal" the bridge. After the calibration above, one applies a precision shunt resistor to unbalance the bridge, and notes the indicated reading in lbf, based on the new fit. The user does a field calibration (or verification) by applying the same shunt resistor, and scaling their system to get the same reading. Best if this shunt resistor is built-into the transducer. A shunt cal accounts for both differences in Vex in the field and any gain errors in the data system used. In old days, some used multiple shunt resistors to correct for non-linearities in the data system, but unneeded today since voltage calibrators are readily available.
It sounds like you are asking about an actual calibration with weights, as is done in the manufacturer's cal. One would apply 2 weights (first could be 0 lbf) and records the (mV/Vex) signal (s) for each, then determines the span number: (lbf2-lbf1)/(s2-s1). From Beckhoff's screen, it appears they have a function block that can automatically apply an actual weight at peridodic intervals. There must be a digital output to make this happen. I imagine they take care of all the math and reading the module. I have some ES3351 modules that I will use soon, so I'll try it myself.
