Sensing with a voltage divider circuit
One of the resistors has a fixed value, the other one is the sensor resistance and its value depends on the measurement.
Only if both resistors are of comparable magnitude it makes sense to do a measurement, as otherwise a small change in the sensor resistance will cause either a very large or a very small difference in the output voltage.
In other words, the sensitivity factor is optimal when both resistors have a comparable magnitude.
Dependent of temperature
Resistive sensors are in general not stable with temperature. Suppose you are using a strain sensor.
If the temperature changes, the output voltage change of the sensor caused by the temperature change is independent of the strain you are measuring.
If the sensor change is very small, you need a very stable voltage supply in order to use the measurement circuit as depicted in the figure above.
The output of a strain sensor, for example, might change only a percent.
If the voltage input has fluctuations in the same order of magnitude, it becomes impossible to do a useful measurement.
A solution for this is to use a Wheatstone bridge