Of course that'll be the straight-line strength, one should probably knock off 2/5 for knots or fixings applied to the rope, and then divide by five to get a loading which takes into account that it won't be a static load, which gives 87 kg for the 7/64" and 136 kg for the 1/8" (then multiply by two for hammock slings). This is a layman's understanding and I'd be happy to be corrected.
Looking on Hammock Forums, they are recommending the 1/8" for anyone over 400 lbs (180kg). I am around the 100kg mark and have been using the 7/64" for the last two months with no issues, but I am using Whoopie slings through the hammock channels to a Nacrabiner on the tree hugger loops.