Thickness?

Is the thickness of the board only related with buoyancy? Does it also effect the turning ability?
If I'm downsizing, what's a good size? I've been riding 9'1" x 22 3/4" x 3 3/8"
I'm looking at this second hand board - size 6'8" x 22" x 3 3/8" with flat base.
How would this be? I'm roughly 180 pounds. Should I be looking at something narrower and thinner? I ride about twice a week if it matters..
If I'm downsizing, what's a good size? I've been riding 9'1" x 22 3/4" x 3 3/8"
I'm looking at this second hand board - size 6'8" x 22" x 3 3/8" with flat base.
How would this be? I'm roughly 180 pounds. Should I be looking at something narrower and thinner? I ride about twice a week if it matters..