There are professional climbers who are 'heavy'.

Finger strength, overall strength, flexibility, coordination, balance, and technique all play a massive role as well.

I don't know why the bodybuilders I've climbed with seem to be worse than overweight/obese people I've seen climbing for their first time, but I've had this observation as well.

The main "trick" to climbing is to use good technique and not muscle your way through. Even fat people can climb.

The fat old climber is some inspiration. https://explorersweb.com/fat-old-climber-gordon-robb/

There is a pot-belly 35 year old at my bouldering gym that is better at overhangs than most of the people there, including myself.

Some of these guys can do pullups all day, but they only train within a strict range of motion and they aren't necessarily any good at doing anything outside of that range.

When I started climbing I could do 3 pullups, and now I can do 18 in a set. I don't train pull-ups, just climbing.