I'll add my agreement that wheels matter for us big people. As I said above, I'm 6'3" and 255 lbs. Everything I own and ride is old lugged steel, ranging in age from the mid-1960s to the early 1980s. I have zero worries about the frames. But I also insist on wheels with 32 or 36 spokes. I simply do not do minimally-spoked wheels.

With 32 or 36 spokes, if a spoke breaks. I can make it home, maybe without even having to open the brake calipers. (I know because I've done it, although it has been quite a few years since I busted a spoke.) However, with a low-spoke count wheel, each spoke is under much higher tension and thus the wheel will deflect much more if a spoke goes, and you will either have to do a serious roadside truing job or call for someone to come get you in a car. (I know because I've seen it happen and have done emergency true jobs on such wheels in the middle of a ride.)

I also now ride 32mm tires on all ,y bikes on whoch they will fit, not for weight-nearing reasons, but because they are more comfortable.