The reaction stoichiometric coefficients do not say which component is most affected by the change, but rather which component pressure/concentration has the biggest impact on the reaction quotient(*)
With temperature change of the equilibrium constant, the component with higher order of power have equlibrium presure/concentration less affected, as it is boosted by the exponent.
The reaction stoichiometric coefficients say nothing about the ratio of pressures nor concentrations of $\ce{A}$ and $\ce{B}$. They just say 1 molecule of $\ce{A}$ forms 2 molecules of $\ce{B}$ and vice versa.
But, they determine the exponents in the expression for $K_c$ or $K_p$.
$$K_c = \frac{{[\ce{B}]}^2}{[\ce{A}]} \tag{1}$$
$$K_p = \frac{({p_{\ce{B}})}^2}{p_{\ce{A}}} \tag{2}$$
Increasing of pressure causes the right side becoming bigger than $K_p$ (and $K_c$ for gaseous phase) and some $\ce{B}$ reacts to form $\ce{A}$ to make them equal again. And vice versa if the pressure decreases.
Imagine two times bigger pressure concentration means four times more frequent $\ce{B-B}$ collisions and four times faster $\ce{A}$ production While $\ce{B}$ is produced just two times faster.
Note that the value of $K_c$ or $K_p$ is irrelevant here, it is covered by the proportionality constants for reaction rates. As the fraction of collisions leading to reaction varies greatly.
See the ice-skating analogy and another question Why are the stoichiometric coefficients the powers in the rate law?
REferring to the linked ice-skating analogy and further elaborating it:
The 3rd $[\ce{A}]$ represents another skater, colliding with a heap.
The frequency of the collisions of a 2-skater heap and another skater is $$k_3[\ce{H}][\ce{S}] \tag{3}$$
The "concentration" of heaps is $$[\ce{H}]=k_1[\ce{S}][\ce{S}], \tag{4}$$
It gives together:
$$k_3k_1[\ce{S}][\ce{S}][\ce{S}] = k_4[\ce{S}]^3 \tag{5}$$
So, the frequency of collisions of skaters with a 2-skater heap is proportional to the third power of skater "concentration".
But better not to interpret how to divide 3 skaters between the same 2 parts.
Be aware of the note in the other post that it is valid for elementary reactions. Complex reactions with various intermediates have more complex relations in reaction kinetics. Bringing the terms from the equilibrium constants to rate equations is not generally valid, as they do not generally describe the opposite directions of the same elementary reaction.
(*) - the expression for reaction equilibrium constant, but with current values for the reaction, being generally not in equilibrium
