To keep warm I use my sleeping pad in my hammock (I built a double layered hammock, so I have a "pocket" built in to hold the pad. It's not really extra weight, as I had to have two layers, since I was using thin material and it wouldn't hold up if I just had the one.)
Not only do I use my sleeping pad, but I can string my poncho up underneath the hammock for a windblock. My quilt/blanket/sleeping bag goes over-top of me. I sleep in my thermals, and carry a thick pair of socks just for sleeping in. A toboggan on the head makes a great difference. Using this setup, I've slept comfortably down to around freezing (about 35ish).
As for the bugnet, mine is an army surplus net that I got somewhere. It just hangs down around the hammock, which is great because I can get in/out on either side and can remove it completely if I don't need it. During the day the bugs aren't too bad, it's just at night when they start coming out, so I can leave the net off until I need it. Mine has a couple of strings attached around the edges, so I can tie it closed if it's going to be windy.