You have to get into the math a little bit to understand this one, and it has to do with this equation. I put in some dots spacing.
R = V-squared.....
.....g * tan(theta)
where:
R= radius of turn
g= gravity
V= velocity of airplane (speed)
theta= bank angle (zero is no bank)
So, in a level turn weight must equal gravity, and bank angle is constant as well by definition, then what must happen to R with a change in speed (V)?