Bridge circuit and the error caused by a differential amplifier
The analysis is fairly straightforward. (BTW, it would be really helpful if your diagram included reference designators on the components so that it would be easier to talk about them.)

Consider the two resistors connected to the noninverting input of the opamp. Clearly, the voltage at that input will be V2/2. The feedback action of the opamp will make sure that the voltage at the inverting input is exactly the same. In terms of loading on the bridge, you can think of the two inputs as being shorted together.

The differential load on the bridge is therefore 2&times;R &mdash; the two input resistors in series. There is also a common-mode load on each side of the bridge that pulls both V1 and V2 down. This is also 2&times;R. These resistances are in parallel with the lower legs of the bridge, and will have an effect on the balance of the bridge unless the two sides have nominally equal impedance, as yours does.