As others have already noted, keeping out mosquitos can be a big deal in some locations at some times of the year. However, when I go camping around Arizona in the summer that's not the reason that I use a small tent instead of a tarp.
The biggest reason in this case is larger critters that can hurt you, like rattlesnakes, scorpions, and the like. Some of these can sense radiated heat and home in on it. You really don't want to wake up with a rattlesnake in your sleeping bag.
A tent protecting you from large preditors is overrated. First, it wouldn't really protect you if the predator was determined. But the real issue is that such things just aren't a credible threat in most places. What exactly are you afraid of? The most common animal large enough to damage a human in places I've camped is a black bear. Except for a few very very rare isolated cases, these just don't attack humans. I have encountered black bears in the wild on several occasions, and they have bolted each time they saw me. Most likely I have encountered them many more times, except that they saw me first so that I was never aware of them.
In some parts of the world, predators are a issue, but not where most people camp. I hear polar bears in the arctic can be a real danger, and so can some of the predators of central Africa. But here in the lower 48 US states with very few exceptions there is nothing out there that will try to eat you in the night. Grizzly bears can be dangerous, but not because they want to eat you. People have gotten mauled because they camped right in the middle of one of their paths, thereby making it a territorial issue. A thin layer of nylon isn't going to make any difference in that case.
I have camped with a tarp in the White Mountains of NH, and not even a tarp a few times around New England. Safety was never a issue. One time I did wish I had a tent with me in summer on Cape Cod due to lots of mosquitos. I tried to cover myself including my face as best as possible, but this was difficult because I still had to breath and because it was quite warm. I'm sure I got bitten numerous times in the night. There was one upside of that though. The next morning when I woke up enough to think about the mosquitos I realized to my astonishment that I couldn't find a single bite on me anywhere. I found out later that extensive exposure to mosquito bites can actually lead to some immunity. Now when a mosquito bites me, it will itch for a little while, then in 20 minutes it's completely gone and I can't even tell anymore where the bite was.
I wouldn't recommend deliberately going out and getting bit by lots of mosquitos to get this immunity. They can carry disease, and I was lucky that I wasn't infected with anything bad. But, it has been nice to not be bothered by the little buggers that much.
Another point is that the right kind of tent will give you protection from rain, bugs, and creapy crawlies, but doesn't have to be any heavier than a tarp. The one I have is just big enough for me to lie down in, and I think weighs less than tarps I have used. It is less than 8 feet long: