After thinking about this all day and looking at some links and posts at hammockforums.net, I finally came across this: http://www.imrisk.com/hammock/ultraquarterweight.htm.
I had an extra Coghlan's mosquito net laying around sized 48"x72" (not sure of the weight; it isn't much, but I don't have a scale right now). As a proof of concept I taped the netting to the side of my hammock, then draped it across to see if it is wide enough. I will have to do further tests with this, as I don't really have a place to hang my hammock inside my apartment (I could try to find a spot on one of the trees outside, but the neighbors already think I'm weird for riding a unicycle, and it is the middle of the night...), but it appears that the netting will be almost the right size for a minimal weight cost. As opposed to the NoSeeUm netting, which has extremely fine mesh, the mosquito netting has wider spacing, thus lower weight. I suppose that means that it could let some small critters in, but I am most worried about dealing with the skeeters right now.
I'm going to try to test this outside sometime this weekend to see what the coverage really looks like, and whether or not it hangs into my face. I hope this works out -- this netting doesn't weigh more than 3-4 oz., so it would be a much better alternative to most of the 8-16 oz solutions I've come across today.