To the OP Pre-stretch them. Find a way to find mechanical advantage, some leverage, and get tighten up the weave by heavily loading them, but within their strenght rating.
To RamblinRev: Because he alread has them. Nobody is taking issue with Ed Speer. He shows multiple wraps around trees.
Sure the OP can do better and lighter. We all can.
To Dutch: Maybe they use nylon because across the distribution of failure modes, nylon stretching provides good warning. Put a 280 lb person in a hammock and being lowered to the gound is non-catastrophic notice that he's at the limits of the system. The stretch in nylon fiber is very linear with fraction of rated load, beginning right with away with even small loads. It absorbs shock well, which is better than suddenly ripping of the polyester fabric in the hammock or failure of the cheap metal hardware when beer buddy climbs on or 50lb kid jumps in, too.