Hi Geertjan,
The Metaball is like a structure or raster in space. The points/vertices of objects are seen as “fields”, (except for primitive-spheres). The calculation is based on both. In the moment you move an object inside of Metaballs, it moves in this structure and creates dat for this raster like spatial (virtual) mesh.
Given the scene of yours, the small element will show more of this structure than the larger one. Here would be my first idea for your scene, move the camera and the large object, so the change of the small object is less noticeable.
Since I write in an forum, even I assume you know that, let me add this: the editor view is always way more rough than the render in the picture viewer for this, based on the Editor/render default settings. Check always the Picture Viewer Render.
I mentioned primitive or parametrical spheres, it is much easier to set things up with those. The overall shape of the Metaball might be then in need of adjustments, FFD cage deformer.
There is a fine balance between the final render mesh of the Metaballs, the Cloth subdivision (if any sub-div at all) and the HyperNURBS or now SubDivision Surface.
I tried as well to use Cloth first then Subdivision Surface, and the other way around. Each time with different values in the mix. The best I have found is in the scene file. Cloth on top of it.
To get objects “thickness” I tied as well the Explosion Effect, but it showed artifacts.
In the render, it might show “bandings”, at least I expect it to show up after compression, but the artifacts I couldn’t get rid off where more light based than Phong based, so I dialed in a different “Details>Contrast Value. You might check it that works for you.
In file _01, I got two little areas with artifacts, in the contact region, around frame 45/46, the file _02 doesn’t shows it, but I had to get the Render Subdivision to 6 cm, you might find the sweet spot. It is a fine balance, as mentioned of the initial mesh, how it is smoothed and then used by the Cloth.
Scene file
_01
https://www.amazon.com/clouddrive/share/OhcQuupOUb6ijwtSy1PqFBfOnHqa7I0GQ18cMdw5xrn?ref_=cd_ph_share_link_copy
_02
https://www.amazon.com/clouddrive/share/nme566W9OpIh4gb6jPbOjszj934q0161zn18uNGjDkn?ref_=cd_ph_share_link_copy
Preview clip
_01
https://www.amazon.com/clouddrive/share/obsmbLEc1gnjLqr07ukhD8DnHtD0A4QP2HQOEB0KZw1?ref_=cd_ph_share_link_copy
My alternative (_03) would be to not use the Cloth at all. My suggestion in this case would, just to fold the “new” (boole based border) and create the “thickness” with a Plain Effector, set to Deform Point and Falloff Linear. See file _03. BTW, it needs (roughly) only half of the polygons to do it, than the ones above.
Scene file
_03
https://www.amazon.com/clouddrive/share/cAvK9VVAVhCMFDJDWvsOYchJ6hw4K2U8Vo4Vy5IA1Xw?ref_=cd_ph_share_link_copy
Preview clip
_03
https://www.amazon.com/clouddrive/share/jLUIYztqu96j5hKGWjHLcoVZIVF01bMbmmeytF2q09e?ref_=cd_ph_share_link_copy
All the best
