Newton rings.
Nite that your solution works (and indeed I use it frequently) for reflective materials. The problem with (e.g.) prints isn't just Newton rings, but also (even more so) issues like uneven exposure across the print if the paper isn't perfectly flat - think of wavy FB or alt process prints. I generally use the foam-padded pressure mat that came with my scanner and weigh it down with something reasonably heavy that's handy. A couple of pounds does the trick. There's very little point in weighting down the entire scanner lid (just leave it up/open) and in fact you don't want to do that especially if you have a transparency unit in there. Weighting down the lid is ineffective and may damage it.