Shielding for Load cells
The typical signal from a typical full-bridge load cell can be in the microvolt range and sometimes quite possibly as high as several hundred millivolts. Noise can affect all levels but is obviously going to be more problematic when the signal is small.

Screened cable with quad twisted cores is part of the solution to noise pick-up but, it sounds like the interference you are picking up is RF and might be also dealt with by appropriate low pass filters before the amplifier used to interface to the load cell.

If you are using an instrumentation amp, these are commonly affected by RF interference and so there are several well-documented options open to you.