Here's my clyde bike. I'm currently around 255 lbs. I'm on the way down at present, and 255 is actually about the least I've been for most of the last 10 years.
It's a Lynskey R260 titanium, disk brakes, Shimano Di2 drive train. I've got a 46cm handlebar on it, a Brooks B17 saddle (love), and a set of custom wheels that I built myself. I call them the AeroClyde wheelset. The tires on the bike are Compass (now Rene Herse) Stampede Pass tires, which are 32mm wide (nominal).
The wheels are made with LightBicycle rims, 46mm deep and something like 28 or 29mm wide, drilled for 36 spokes both front and rear. I used White Industries CLD hubs. The front spokes are aero spokes, the rear ones are standard double-butted round spokes. I'm assuming that the LightBicycle rims are pretty tough, and with 36 spokes both fore and aft these wheels feel like they will be durable as hell being ridden by a very heavy rider, while also being about as lightweight and aerodynamic as any semi-deep carbon wheelset built for a very heavy Clydesdale has any chance of being. You're simply not going to find a commercially offered semi-deep carbon wheelset built with enough spokes to be sensible for a very heavy rider.
