How to talk sensitively about a weight limit for a group activity?

One of my friends and I have been going indoor rock climbing frequently this summer. A few of our mutual friends have expressed interest in joining, including one who self-identifies as fat. There is a weight limit at the climbing gym and I’m not sure if everyone is below it. I don’t know how to bring this up with my friend in a tactful way that doesn’t involve asking his weight, passive-aggressively sending him the height/weight info on the website, or outright excluding him.

My personal belief is that things should just be built so that the majority of the population can use them. I don’t think that climbing gyms should have weight limits because they should just be built so that any size person can enjoy the activity. Plenty of fat people are far more athletic than I am. But unfortunately people who build climbing gyms and gear don’t share this attitude and there are weight limits, and I know it’s not safe to exceed them when equipment is built for a narrow range of sizes.

Can anyone help me handle this in a dignified and respectful way? I don’t want to make my friend feel bad, be fatphobic, and I also don’t want to be dishonest and create a situation in which they have a humiliating experience of being asked to get on a scale at the gym or something like that.

Serious and respectful responses only please. Preferably I’d like to hear from fat and plus sized people.