Why does a sharp leading edge result in a larger pressure peak?
Envisioning the air flow at 15 degrees AoA is very helpful in understanding the negative pressure distribution on the upper wing.  Smoke in wind tunnels is used so the airflow pattern can be seen.  Yes, it is illogical for a thinner wing to have a higher pressure peak,
but notice the TOTAL negative pressure area of both 4408 and 4415 is very close.

What is going on here is the larger frontal area of the 4415 creates a larger, but not as low pressure bubble at 15 degrees AOA (look at graph) than the 4408.  Try superimposing the two airfoils at 15 degrees angle of attack and also throw in a flat plate too.

Remember, a higher pressure peak does not mean higher total negative pressure.  It means, like @Jan Hudec says, air molecules, which have mass and velocity (inertia), can not turn a sharp corner as easily as a small turn.

Imagine 20 race cars going down the track together.  They will make a small turn together, but if too fast into a very sharp curve, there will be a vacuum peak (lack) of cars on the near side of the turn!