I think point of failure for most heavy riders are the wheels.
That would be mechanical point of failure.
I would advise 36 spoke wheels and double wall rims.
That said I bought a bikes direct bike equipped with 32 spoke wheels and double wall rims and they held up fine. I put about 100 miles on them at 325-330 pounds.
Looking back I wish I would have gotten a used Raleigh with steel rims and 36 spoke wheels (if a 40/32 wheeled one was available I would have gotten that instead).
I bought a pair Of Raleigh sports hybrid bikes circa 1975-1985 ish an the wheels they came on seem very rock solid. Steel rims/hubs/spokes 36 per wheel. I gave one to my father and one to my sister. I road my father's bike at least 100 miles both off and on road and no problems at all with the wheels (or an part for that matter).
Both bikes seemed to be nearly unridden and after a checkup and lube up were deemed rideable by my decision.
Just as important as wheels would be tires. Big tires provide more cushioning to the wheels, in my opinion. As a heavy rider who lives in an area with generally bumpy roads I ride the biggest tires that fit my road bike. 700x30 brontager satellite LS if I remember right. I upgraded to a 29er from bikes direct and put that same set of tires on it. Though I could go much larger of a tire I feel the 700x30 brontagers are adequate. I have also lost 40 pounds so I dont ask as much from my tires and wheels.
36 spokes
Double wall rims
Larger tires
Maybe thorn resistant tubes
Just my opinion.
On my road bike I tacod the rear wheel and replaced
It with a "sta-tru" brand double wall 36 spoke wheel that had no problem supporting me at my heaviest. If you or your friend like the bike you described, but are worried about asking too much from your wheels, consider getting a set of those double wall 36 spoke sta-trus. Bike store charged me around 80 for the wheel and swap of the freewheel. If you went ahead and purchased a strong wheelset with the bike from day one, then you would have a backup wheel set that came original.
Just a thought.
No doubt that strategy may be prohibitively costly, but if you got a used bike and a new wheelset you may stay within your budget.
I am a fan of used bikes though; reduce, re-use, recycle.