A flexible reed will flow more air than a stiffer reed at lower RPMs increasing low and midrange acceleration. But at higher RPMs, this flexible reed will flutter thereby no longer controlling the airflow so a stiffer reed will be required. A stiffer reed however will flow less air at lower RPM thereby hurting low and midrange acceleration. Multiple stage reeds have been produced to overcome this tradeoff by combining a stiff reed with openings in it and a flexible reed on top of the stiff reed to cover these openings. Notice that we have said nothing about the thickness of the reed.
Most tuners talk about thicker reeds when they are actually referring to stiffer reeds.
But with the newer carbon fiber reeds, stiffness can be increased without increasing the thickness. The response of a reed is primarily determined by how much the reed weighs. Basic physics says anything lighter will accelerate faster than something heavier. 7000 RPM requires a reed to open and close 7000 times per minute. This is quite a significant amount of accelerating and decelerating in a short amount of time so a few grams can make a huge difference.