Parametric scale of sketch or body?

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Hi Fusioners.
I'm new to Fusion 360 and I'm practising by modelling a chess set, that I plan (hope) to laser cut at some point.
I ran into some unexpected difficulty, that I can't find a solution to in a lot of Youtube tutorials and forum posts here. I may be using the wrong terms...
I 'simply' wish to be able to dimension the design using parameters, as I'm not sure exactly what's possible and how big I want it.
I have imported the profiles that are simple 2d contours, consisting of splines and lines that I want to extrude to flat bodies. I'd like these bodies to be scalable by parameter, so I can easily test different sizes of the design. In this particular design, some lines should coincide exactly with other lines, so the scale has to be exact. And the manual scale function seems to be rather limited.
If a parametric scale can be done on the sketch, I think I can figure out the rest. But if it has to be on a body, there might be an additional problem (I imagine, depending on the solution).
One parameter controls the 2d scale (x and y), whereas the thickness of the material (z) is another parameter. Is it possible to somehow parametrically scale a body differently on the three axises?
Thanks for any suggestions, hints, corrections or links to relevant forum posts or video tutorials, etc.
Best, Asser.