Lightweight tent recommendations?

Tyvek and another ultralite one I didn't like. The best ones I have used are a super cheap and heavy blue tarp thing and an actual tent groundsheet with reinforced peg holes (that was from a different shaped tent). You want something that will fold easily and be able to take plenty of wear and tear. Doesn't even really have to be the exact dimensions of the tent, just fold it under. I have also used a groundsheet as a separate place to sit, improvised rear mudguard, windguard etc. Everything depends on the conditions you camp in/on from shit to perfect. The point is to protect your tent floor and maybe give you a clean floor for the porch area, no need to overthink it.

polycro?

Polycro comes in different thicknesses. Apparently, it is better to get the 1.5 mm rather than the more common 0.75 mm grade.

There are some useful construction techniques, here:
https://backpackinglight.com/forums/topic/how-to-make-a-polycryo-a-frame-tarp

I have read reports of Tyvek leaking at pressure points, e.g., when kneeling. On the other hand Polycro seems to be less durable.