The lightest "webbing" that I've found is about an inch wide and they use it to strap lumber for delivery. Its a plastic material - light and strong. As for strength and speed, I use 2 light carabiners to join everything up. I could set my hammock up in 2 minutes easily but the tarp might take 15.
Jim
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These are my own opinions based on wisdom earned through many wrong decisions. Your mileage may vary.