Common mode voltage range of the INA128, for 5V operation, is 1.7V to 3.6V (typical) per the datasheet. What that means is that the output of the amp never goes from 0V to 5V -- it goes from 1.7V to 3.6V. This limited voltage range is typical for OpAmps and InAmps.
When setting the gain, with too little gain and you'll always see ~1.7V. Too much gain and you'll always see ~3.6V. That should make sense, right? Because with too little gain you won't see any voltage change and the output will sit at the bottom of the range, and with too much gain it'll just be oversaturated and maxed out. You need to keep fiddling with the resistance that sets the gain until you see a voltage "in between" and then you'll start seeing varying output when you push on the load cell.