Op-amp gain decrease, output not linear
If you are powering between 5V and ground, I suspect that the voltage on the positive input of the  TL081 comning from the RTD is too close to rail to be a valid input.  The other arm of your amp is probably having the same issue You are out of the allowed common mode range for that op-amp.  

See table 6.6 on the relevant data sheet.  \$V_{ICR}\$ is volts from the negative rail.

You should use a RRIO op-amp.  The  TL081 is not suitable for this use.