does added mass affect tt speed?

I was considering a "Stablilzer" for a Thorens TD-850 tt. The "stablizers" appear to be primarily weights. They could not slow down platter speeed, or no one would buy them. Are the motors of modern turntables synced, somehow, to an exact speed (as presumably, all those "phase-locked loop" direct drive tt's of yore were) so the heavier platter just takes longer to get to the correct speed and, with the added mass, has more resistance to speed variation? Also, re: platter speed, why isn't the circumference of the pulley on top of the motor, driving the belt, an absolutely critical spec? Most don't look like they are machined to any great tolerance.