Low voltage meters typically require a probe, that is connected directly to the Device Under Test, before long cables go to the meter. I.e. the amplifier has to be detached from the meter. The probe must be very close to the DUT, every millimeter of a wire tends to collect noise from the ambient, that can exceed the voltage to measure.
Without further information I don't know how far a load cell amplifier is applicable in your project. If you already have finished the meter part, you only need a low noise pre-amplifier.