Here is a vid of hammock tensile tests, they stretch beyond recognition long before they actually fail (the 7/64 (2.5mm) amsteel actually snapped before the hammock (1.8 oz/yd^2 fabric, single layer). Amsteel is of course as strong as steel braid for a given diameter, as you can see it took a massive 734KG to fail, if that is the concern.
[video=youtube;7yITshmzIX4]https://www.youtube.com/watch?v=7yITshmzIX4[/video]
If you check warbonnet's website you will see fabric weight is a case of comfort (due to stretch) and be able to see what thickness of fabric will be most comfortable for his weight. If the fabric stretches the lay is compromised and his legs will either hyper extend a little or a ridge will form under his knees (the same effect as incorrect hang angle or unsuitable hammock length/width), neither are fun but are somewhat manageable and can be worked around to some degree (jam a jacket under his knees).
If i where him i would be mostly concerned about length and width due to his height. He won't get truly comfy in a sub 3m hammock at 6ft+, especially if it's under 1.5m wide. When i say comfy, i mean as comfy as they should be, he will get by somewhat in a shorter hammock with the same workaround as above (RE stretch). i'm 6"1 / 70kg and ended up making an 11' hammock (3.3mx1.6m +/-) out of 1.5 oz/yd^2 pertex to get a truly comfortable hang because at the time i thought the uk hammocks and warbonnets where a rip off (in hindsight the price is fair). Too short and his knees will hurt unless he hangs it real tight as there simply wont be enough room for him to get a flat lay. On a tight (sub 30 degree) hang angle load is amplified at the fixings though and they will become a likely fail point. At his size i wouldn't risk a sub 30 degree hang angle so i think he should get as long as he can afford/find. He might find a 10 footer to be long enough to avoid leg hyper extension at a 30 degree hang angle, i went with 11' to play it safe.
Double 1.5 fabric will possibly be fine but i wouldn't unless it was purely to test the water as it could stretch, double 1.7 or 1.9 i would bet on it he won't notice stretch while stationary. Very large folk from the US swear by double 1.7 or 1.9 on hammock forum. As mentioned though if in doubt you can check warbonnets site
http://www.warbonnetoutdoors.com/www.warbonnetoutdoors.com/hammocks-101/ , or better yet ask the same question over at
https://hammockforums.net/forum/content.php .
TW double layer hornets are very thick fabric, i have one i no longer use (if he ships it he can borrow it to try), prob well over 2 oz/yd^2 nylon and comes in double layer. Also cheap, very cheap. I have had three people of similar weight to me in one with minor stretch (although my rigging was on the brink). Too short though imho @ 2.8 meters, i don't use mine any more because i kept having to stretch it out to rid myself of leg hyper extension. They sell a longer version now @ 3m, that might be right up his street if the fabric is the same as the hornet. Be warned though, they are stupidly heavy/bulky as are some of the DD's and i don't trust the guy who runs TW to be honest as he doesnt publish essential information like fabric weights (which he surely can get) and has clearly misleading product information on his site that appeals to those who would not know better (or at least he use to, as did DD, but not checked his site in a while so YMMV).
ENO at last count where also releasing a longer hammock, in what fabric i do not know, but their prices are comparable to DD/TW and their product line has been vastly improving in recent months.
If he increases budget though, or ends up really loving em and wanting top end i would recommend the UK hammocks expedition. Currently £130 but i assure you after making one in quality fabric that is well priced. Quality fabric, plenty of length/width, quality design, structural ridgeline and adjustable footbox. BUT, they are heavier than his woodsman X. DD/TW/ENO, damn, even hennessy don't compare. I would put money on it that the expedition is more than comfortable for him, but quality and comfort costs. Sure, the single layer 3oz fabric equates to double 1.5, not thick enough right? Well it actually might be, it depends on the type of weave too, not just fabric weight; email him and ask, matt is a good maker who knows his products and would probably make it in a suitable fabric for the extra cost of materials if needed. He has not flinched over me asking for custom work in the past and his quotes where highly reasonable. See:
http://ukhammocks.co.uk/products/woodsman-xpedition-hammock?variant=1031233356
There is also the warbonnet blackbird XLC in varying fabric options (double 1.7 being the one to note) which is well reputed, but even more expensive after import for little benefit over the expedition (removable bug net and optional winter screen).
http://www.warbonnetoutdoors.com/blackbird-xlc/
I think dutch also does a longer hammock in argon fabric, but if i am honest i find dutches quality control poor/inconsistent, his sewing skills are clearly lacking and the way he deals with issues from overseas customers (in my case at least) is frankly appalling (he is reluctant to replace due to shipping etc and tries to offer partial refunds as a compromise). Dutch is highly over rated quality wise, but he has some clever ideas in terms of hardware design and the cost of his sewn items is relatively decent in some cases. YMMV, that is simply my experience with him.
A quite common thing is also to simply buy a large nylon.polyester tablecloth and 'whip' the ends, assuming he is not bothered about a bug net he can pick and choose size and fabric on a budget. If he goes with polyester he will need to 'up' the fabric weight a little, apparantly it's not as quite strong for the weight but has lower stretch, so they say over at HF anyhow.
Hope this wall of text is of some help, there is far more to hammocks than first meets the eye and frankly they can be a real headache, but it pays off.