High Precision ADC/DAC Circuit Feedback
You're using a voltage divider.  The Wheatstone bridge is simply TWO voltage dividers in parallel, with the non-sensor side just providing a baseline.  

This provides two main advantages.  First, the Wheatstone bridge facilitates a differential voltage measurement, as opposed to a single-ended measurement.  If you're careful with your wiring, this means that much of the noise on the positive and negative ADC inputs will be common mode noise, and the common-mode rejection of the ADC can attenuate it.  Second, The differential nature of the input signal of the Wheatstone Bridge makes it easier to amplify (either with ADC options, if they are available, or with an external amplifier), helping you to more easily use the whole dynamic range of your ADC.

As a fine point, the bridge provides you with the opportunity to servo-drive the excitation voltage if you use the right kind of amplifier, which can really help when there are long cables between your sensor and your circuit.  The mechanism is shown in figure 2.15 of http://www.analog.com/media/en/training-seminars/design-handbooks/49470200sscsect2.PDF, and works on the principle that there is essentially zero current in the sense line, so it makes no difference how long the cable is.