Strange Behaviour Using LM358 Op-Amp as Wheatstone Bridge Difference Ampliflier
You want a circuit with high impedance inputs so as not to load the bridge. You can  use this circuit if you want to stay with the LM358 (requires 1.5 chips):



The offset voltage and TCVos is rather high on the LM358 though (maybe 3-10uV/K) so you may wish to use a better amplifier such as a 'zero drift' instrumentation amplifier. 

Also 3.3V is barely enough voltage to power an LM358 so  you will get very limited input common mode range (as bad as 0V to 0V over temperature), so in fact it is most certainly not guaranteed to work- you are lucky it's functioning at all. If you must use this kind of amplifier at least give it 5V or more to work with.