Hammock camping can be lightweight, but in my experience the lightest hammocks usually have a comfort tradeoff.
My hammock setup (SDL Trail Lair, whoopie sling suspension, silnylon tarp) is slightly heavier than my tarptent (Double Rainbow), but the hammock is MUCH more comfortable to sleep in, and I can sleep in locations that would not be possible with a tent (over rocks, slanted ground, even a stream).
I also don't need to carry a sleeping pad anymore (I have an underquilt instead).
I started out with an ENO doublenest, and while its fun and comfortable to relax in, I couldnt sleep very well in it. The Eno's are short hammocks. Most of them are 9'4" long. My Trail Lair is 12 feet long. In general, the longer the hammock, the easier it is to get a relaxed diagonal lay (this enables you to sleep very flat). When sleeping diagonally in shorter hammocks, there is a tendency to get midline pressure on your calf, and this bothered me a great deal in the Eno.
There are better options than ENO. Look at the cottage industry makers like Simply Light Designs, Warbonnet, and Dream Hammock. Eno tarps are a bit on the heavy side also.