DIAGNOSIS This is a classic sign of a failing turntable motor. The motor gets weak and can't overcome the initial inertia of a loaded plate, so it stalls after a brief attempt.
FIX First, rule out the simple stuff. Unplug the microwave, take out the turntable and roller ring, and wash them. Check the hub in the floor of the cavity—make sure it's clean and spins freely by hand. If the hub is fine, the motor is under the floor. To test it, you'll need to remove the outer cabinet. Once you have access, disconnect the motor's wires and apply 120V AC directly to it (carefully, with alligator clips). If it doesn't run smoothly, the motor needs replacing.
IF THAT DIDN'T WORK If the motor runs when tested directly, the problem could be the main control board not sending consistent power to the motor. This is less common than motor failure, but it happens.
HEADS UP When installing the new turntable motor, make sure the drive coupling is aligned correctly with the hub in the cavity floor. Forcing it can break the new motor's plastic gears. The motor should just slide into place without a fight.