

How you judge your sleep massively influences how you feel, so I always judge how I slept, then check the watch if it agrees. If I think I slept well and the watch says no, I say technical malfunction. If I felt I slept bad and the watch says I slept well, I feel better about my sleep. Win win

My boyfriend is 6’7 and weighed about the same as you when he started climbing (120 kilo). For climbing with ropes, I would advice a partner that is no more than 20 kilos different than you to start, as it is difficult to belay. I don’t know about autobelay systems, but I am sure you can ask their weight limits. The easiest would be to start with bouldering, as you don’t need ropes and the routes are short. (Which is easier for stronger heavier builds)
Rental shoes might be a problem as climbing shoes are often a slim fit. Maybe investing in a beginner pair works better for you than renting.
Every climbing gym I’ve been to has had a friendly and open atmosphere. People of all different shapes and sizes and levels were mixing and helping each other find the best ways to climb. So please go give it a try.
Finally, as a strong person, please take care of your fingers. In climbing, a lot of weight goes into those and the stronger you are, the easier it is to get injuries. So warm up your fingers by gently pulling on some holds and doing easy moves before you get into the hard stuff.