If a sewing machine or sewing is your reservation for DIY, you can make a tablecloth hammock without any sewing, by whipping the ends. By far the cheapest and easiest way to start hanging, and wouldn't take you more than a half hour of work, and that includes some researching around these forums on whipping how-to.
The fabric seems strong enough to support you without adding on an extra layer. I have had the whole family in mine (the 90" wide version) easily over 375lbs, and I felt it could have held more.
You will probably want a wider hammock. "how wide" is a very subjective question, but the 60" X 126" size tablecloths would be a good size to start. I definitely wouldn't go lower than that.
I also have an ENO doublenest which has also held the whole family without effort. Great little hammock, very light, and comfy. It has a much more silky and stretchy fabric than the taffeta tablecloths. I will mention, that the ENO's are a tad shorter by comparison (mine is even shorter than their advertised length), so it might be more difficult to find that 'sweet spot' on an ENO with your height.
Good luck with your quest!