A hammock is a small enough space you need some ventilation to prevent condensation.  So you need some space/opening above you to let the moisture out.  That said the Hennessey comes with a very small tarp that fits very close to the bug screen.  I have a Hennessey and I have never used the tarp it came with because I want a place to get out of the rain other than laying in my hammock.

hi all.
it has been many years since i was on this site. i hope it still has some active members that may be able to help.
i may be heading into quetico back country this summer.
i recently was reading about hammocks that many hikers / paddlers use instead of a tent.
i like the idea but am wondering if anyone knows of a hammock style that also is completely covered like a tent. not just with a rain fly.
i found one called the "flying tent" but am looking for other options. hopefully one that is not so heavy. the flying tent is over 5 lbs. 
if anyone has any direction they could give i would appreciate it. thx  rick