let us consider the centripetal force equation,
centripetal force F = mv² / r
f= force
v= velocity
m= mass
r= radius.
in all the factors only velocity has the power of 2. so when you double the velocity then it will become square of that.
if v= 2v , F = m4v² / r
so velocity is doubled it would produce the greatest change in the centripetal force.