MCP6N11 voltage reference and output problem
You have 3V applied to the inverting input and 2.5V applied to the non-inverting input. Thus, your output should be -1V with a gain of 2 (assuming reference grounded). It should work properly if the amplifier has a reasonable negative supply (say -5V). However, you show no negative supply, so the amplifier cannot work- the best it can do is get within some tens of mV of the negative supply, as shown in the datasheet. 

If you connect the reference to a stiff voltage of 2.5V then it should output 2.5V minus 1.0V or 1.5V with the bridge connected. However you'll need something like a voltage divider plus an op-amp buffer to get the stiff 2.5V supply, a simple voltage divider will not cut it. 

It's really not clear what you are trying to achieve with this. In the particular case here you can simply ground the reference input, swap the inverting and non-inverting inputs and get 1V output, however if you need to handle the bridge being unbalanced in either direction you'll need to bias the output by setting Vref to something other than 0V.