Differential amplifier noise

MarkT:
Filtering out any RF on inputs is always a good idea for sensitive DC circuits like this - 1nF ceramic across all the load-cell input leads
should kill any RF pickup without affecting the frequencies of interest. Ferrite toroid on the whole lead close to the breadboard is
also another possibility.

Definitely keep all the wiring on the breadboard short and neat and supply decoupling capacitors are obligatory
for a high-gain amplifier, otherwise it is very likely to oscillate via supply-rail feedback. A ground-plane would be nice,
though obvious difficult on a breadboard. One can add a grid of ground wires across the whole breadboard to
improve matters.

Reducing the gain in the circuit will reduce risk of instability/oscillation BTW.

I want to try to place a filter to power lines and wheatstone bridge output, it's good 1nF? how i need to connect it, between + and - like a short circuit? but a filter don't need a resistance?