When the current is doubled, the deflection also doubles in

For a moving-coil galvanometer, the deflecting torque is $\tau = NIAB$ and the restoring torque is $\tau_r = C\theta$.

At equilibrium, $NIAB = C\theta \Rightarrow \theta \propto I$.

Thus, when the current is doubled, the deflection also doubles.

For a hot-wire ammeter and a moving-iron ammeter, the deflection $\theta \propto I^2$.

For a tangent galvanometer, the current $I \propto \tan \theta$.