There is no weight limit to climbing, everyone can climb regardless of their weight. Though, those that are overweight may have a higher risk of injury and should be aware of this and be extra careful.
People who weigh more usually tend to have a more difficult time climbing than those who weight less. This is because they need to hold much of their weight on their hands and fingers, which can be very difficult if their fingers are not strong enough to hold this weight and to perform the moves needed for climbing.
Though weight can make climbing more difficult, it doesn't mean you have to be super skinny. There are many great climbers that are on the heavier side, it just means that your fingers and muscles will have to be very strong to be able to pull your weight.
This is all true not just for those who have a high body fat percentage, it is also true for those with a high level of muscle mass. Bodybuilders, for example, may have a difficult time climbing since they will have to pull their whole weight on the wall, which, depending on the size of the bodybuilder, can be a lot.
