Voltage ramp in INA125 output
I'll go out on a limb here, and suggest that you are seeing pickup of a 5 KHz source. I'm assuming you have a pretty high gain - load cells usually have an output of ~ 1 mV / V of excitation, which means you need gains of ~ 1000. Gains this high, combined with the very high input impedance (10^11 ohms) of the INA125, make for extreme susceptibility to pickup. This also would explain why you don't see these pulses elsewhere - at a gain of 1000, they are only 100 uV (riding on half the excitation level) at the source. 

I assume you're using the standard circuit shown in the data sheet: http://www.ti.com/lit/ds/symlink/ina125.pdf

Start by making sure that both the excitation +/- and the output +/- are at least twisted pair, and preferably shielded twisted pair. Second, put a 10 uF non-polarized capacitor across the inputs. Even better, instead of running the load cell directly into the INA125, add a pair of low-pass filters: 10 k to each input and a 1 uF capacitor to ground for each of the inputs. Do this right at the IC. If you put the input filters in, don't bother with the cap across the inputs. 

This will, of course, cut the frequency response of the system somewhat. If you need millisecond response, you'll have to be more careful with your wiring.