Where the weight is being carried and in what form is probably more important than total weight. If you’re 240lbs, short, and it’s all butt, boobs, and belly, that’ll make things tougher all around on the body, not just climbing, but yes that too.
After I got out of the Army, I gained almost 40 pounds of body fat in 2 years. Started having some pain in my lower back, ankles, and knees. Winded climbing stairs, taking breaks in the trees to catch my breath. Sleep was shitty, depression was worse, clothes weren’t fitting well, even sex was lame and tiring. I stopped eating like I was still a 20 year old soldier got back into some exercise routine and now I diet and cardio hard if I see my weight go to 200, and honestly I’m happier and physical labor is way easier if I’m more like 190. I’m 6’. That’s for now... if I ever decide to get off my dead ass and get back into a lifting routine I’ll be happy over 200 if it’s muscle gains.
If you do something to lose weight, pay attention to other aspects of your body and life in general... it was striking what improved that I hadn’t expected.