The meter bridge is very sensitive when the resistance of all four arms of the bridge are off the same order. It is so far moderate resistance only the meter bridge becomes insensitive for too high or too low values of resistances. So , while measuring low resistances, the resistance of copper strips and the connecting wires become comparable to the unknown low resistance and hence cannot be neglected.
If we measure too high resistance and the meter deflection is too small, that is currents are too low.
Similarly
For very low resistance you get errors due to the resistance of the wire and the connections.