Load cell and amplifier
The regulator is the problem - you are exciting the bridge with 12 volts and this means that the typical voltage on the bridge output (to ground) is half this value at 6V.

You are running the chip from 5V and so I suggest you feed the bridge power connection from 5V. The next problem you will have is that the offset (reference) pin of the INA122 is connected to ground and this should ideally be connected to half the power rail of the INA122. This then accommodates a bipolar input range from the bridge. See figure 5 of the data sheet.