Reading thru, it appears you’re basically looking for a large hammock tarp w/ doors, less than 1lb, right? That narrows things down and Andrew has listed a couple good options. I’m almost exclusively a hammock camper and have been dialing in my tarp setup lately so here’s my two cents to maybe help fill in any gaps or affirm others comments.
for most hammockers, “large” (or full coverage) basically means a hex tarp w/ doors or a square tarp that’s st least 9’x9’. so you can ignore smaller rectangular tarps, asym diamond tarps, standard hex tarps (no doors), etc. A hex tarp will be best for a beginner as it’s very straightforward to setup. A square tarp will give a few more pitch options though.
At that larger size, it’s gonna have to be a lighter material to stay under 1lb. Any tarp made w/ material heavier than ~1.3oz/sq yd will be more than you want. The lightest waterproof materials are DCF at .51oz/sq yd, silnylon is ~.7oz/sq yd, silpoly is ~.9oz/sq yd. Others have described those already so I won’t again.
There are a lot of vendors who sell hex tarps w/ doors in lighter weight fabrics. In addition to Andrews list, there’s Dutchware, Simply Light Designs, Zpacks, MLD, Warbonnet Outdoors, etc. Most have square tarps also but one that doesn’t sell hex so not mentioned above is Hyperlite Mountain Gear. Peruse their sites and make note of material vs weight vs cost as they vary substantially. Cheapest 1.3oz sq tarps could be 1lb and $50. Lightest hex tarp w/ doors in .51DCF are 10oz and ~$350.
Side note, the lightest sil-materials get complaints of not being quite 100% waterproof as users experience “misting” underneath them… many believe this is actually just condensation being knocked off by the rain droplets but I haven’t seen anything definitive.
hope that helps point you the right direction.