Here's an off the wall suggestion: build a tensegrity prism using four twelve foot poles and very strong cables (I will probably try this with some 5/16" amsteel I have). Here is a picture of a 4-strut tensegrity prism, albeit very small, and proportioned wrong for a hammock stand. It's a lightweight stove table I use so I can sit in my hammock and cook. In this picture, you need to imagine that there is no kevlar top fabric, the distance between the orange straps is 9ft (this is where you hang your four hammocks), the ridge lines for the hammocks connect the ends of the poles (replacing the tension from the kevlar fabric), and the height of the prism is about 6 ft.
Tensegrities distribute the forces acting on them evenly among all components, so the lines are all under tension (equally) and the struts are all under compression (only - no bending forces). This would probably be the lightest possible support for 4 hammocks, but don't underbuild, because the forces are substantial. You would definitely need a come-along (ratchet hoist) to tighten that last side tendon when assembling it. This little stove table weighs 3 or 4 ounces, but I have to lean on it pretty hard to tighten it down.