I'm trying to scale a physical object up in size, either double or quadruple. It's a circular acrylic plate, with multiple weights attached around it's edge, to lower the resonant frequency to a specific frequency, 32hz.

The plate is 16” in diameter, the weights around it's edge add up to 1.05 kg. It needs to be scaled to 32” or 64”. It will scale in diameter but not thickness, which will remain 1/8” for all diameters.

If the size is doubled to 32”, along with doubling the weights around the edge to 2.1 kg, will the resonant frequency be lowered to the same frequency as the 16” plate with 1.05 kg weights?

If not, how does this scale? How far off approximately will the resonant frequency be from 32hz?

Same question for scaling to 64” with 4.2 kg weights around the edge.

A larger plate would have a lower resonance frequency, and depending on how the weights are suspended and the plate is supported the effect of a given weight will be more dramatic for a larger diameter plate of the same thickness, not less. I think you're going to have to do the experiment to see what values of weights work. This is a complex non-linear problem, and I can't give a more precise answer.