Angular Acceleration and Radius

I am writing a lab report for an experiment where we used a rotary motion sensor with different sized disks to find angular acceleration as a string attached to a falling weight unraveled and accelerated the disk. I am having confusion with my graph results and am wondering if they are correct or something is wrong.

The angular acceleration I find is increasing as the size of the spinning disk increases. From everything I have at my disposal I believe there is an inverse relationship between angular acceleration and the radius of the disk, so as the disk gets bigger the angular acceleration should decrease. Could the string be providing a lot more torque as the disk gets larger? Would you expect the tangential acceleration of the different disks to be constant, or changing as well?

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