One easy, reasonably lightweight fix is to add bug net around the outside hems of the tarp, 2 feet high on the sides and 2' + peak height on the ends. No zipper and no floor. You just lift the net and crawl under. The net drapes on the ground. Mosquitos don't crawl. For 36% lighter weight use Thruhikers Nannoseeum netting. You don't even have to hem the net. It won't unravel.
The net gets wet in the rain. No problem. It catches splashes from the sides, a good thing. It screens some windblown drift, a good thing. It will not exclude bears or anacondas. As long as you don't set up on an ant hill or in a potential mud puddle, not having a floor is an advantage. Water will not pool on the floor. You can move the groundsheet back and cook in a pouring rain.
This option does not let you stargaze. For that, you might consider a simple, floorless net tent that will suspend either from tabs under the fly or independently. Again, no zippers. Look at the design of the old military mosquito bars for use under the GI shelter half. They are like two pyramids separated by a short ridgeline, and give the most coverage for the weight. Unfortunately, they are made with heavy net and weight about 14 ounces. You can make a civilian version for 6-9 ounces, depending on the netting you use and the size (solo or double).