The size of the rotor doesn't, in itself, affect the gyro's speed range. With other things equal, however, RRPM does.
The NACA studies of autogyros back in the 1930's resulted in a statistic that the researchers dubbed the mu ratio (the Greek letter "mu" is pronounced like a kitten's noise: "myoo"). This is simply the ratio of the tip speed of the blades to the forward speed of the gyro. The ratio helps us tease out the drag compromise between high RRPM (limiting retreating-blade stall but risking high advancing-blade drag) and low RRPM (limiting the blades' profile drag but creating a larger retreating-blades-stalled area).
The sweet spot turned out to be around 0.35-0.4. I.e. the blades' tip speed should be about 2.5 times the aircraft's forward speed for maximum efficiency.
Increasing the rotor diameter (with the same blade design and pitch) on a given machine will make the rotor turn slower. This means that the larger-rotor version will hit its maximum efficiency at a lower airspeed.
Of course, by "tip speed" we mean the average tip airspeed or, saying the same thing, the geometric tip speed (RRPM x rotor circumference).
High airframe drag can overwhelm our attempts to optimize mu ratio. For example, the original Bensen B-8M had a 22-foot rotor turning around 400 RPM. Tip speed was therefore 460 ft./sec. or 314 mph. Multiply by an ideal mu of 0.35 and you get an ideal cruise speed of 110 mph! That's only from the rotor's viewpoint, however. The B-8M's open frame is so draggy that almost no amount of horsepower can push it that fast, no matter what the rotor would prefer. Bottom line: for body-drag reasons, Bensens had least-drag airspeeds of 45-50, corresponding to mu=0.2 or less.
IOW, un-streamlined gyros are inefficient. Surprise! We can make even a Bensen a little less inefficient by slowing its rotor down -- which many of us did, back in the day, by pitching them up past the scribe marks and/or swapping for a longer hub bar.
The original Gyrobee takes these tactics a bit farther, using a 24-to-25-foot rotor on a featherweight machine. The resulting gain in efficiency is enough to make a fairly decent gyro using only the 40 hp Rotax engine. Of course, the Rotax's redrive, allowing a big prop, helps, too.