Continuation of this question, apologies for the schematic. Rwire and Roh are depicted in balanced state.
This is a common Constant Temperature Anemometer circuit, however the diff amp output (Vbridge) keeps on saturating. I think the problem is on the INA118 output (Vina). A voltage divider analysis at the bridge would show that if Rwire < Roh / 10 then Vwire < Voh and hence Vina = G(Vwire - Voh) would have different polarity with Vbridge. Similarly, when Vwire > Voh then Vina would have the same polarity with Vbridge.
The table above shows a couple of measurement I did and it can be seen Vwire > Voh for all cases, but Vina have different polarity with Vbridge everytime. This differs with the analysis, I thought the diff amp may be messing with the inamp output but not sure why. Assuming that the components are not broken (I checked but maybe I'm wrong) what else could cause this?