Robert,
to really understand the working of an Op Amp, or Instrumentation Amp, you should read "Design Reference" from Texas Instruments. You can download it from ti.com, just search for SLOD006B. Also read SLAA068A and SLOA030A, etc.
The INA114 was a very good general purpose part years ago. It is not a rail-to-rail unit and is more than 10 years old, there are more modern Op (Instrumentation) Amps available from several manufacturers.
To have the output voltage (going to the ADC) going up or down when applying weight to the sensor is just a matter of switching the two outputs from the sensor (+ or-) going to the Op Amps. Of course you can also handle this in software.
I have used the TLV 2474 (Quad OpAmp) many times for those kind of applications successfully.