Depending on where you typically hang, maybe a couple ft of seatbelt type webbing. Just enough to get you 3/4 around the tree.

I'm new to this but I use 12ft of 1" webbing on either end, tie it to a carabiner that's about 4" long from the hammock. Pack size is important but not critical, and I don't care about weight much as I never hike but motorcycle camp.