Climbing is seen as a sport where getting the best power to weight ratio can help, up to a point. If you drop weight too much then you will lose muscle mass which in turn will not help you climb harder. Instead, look at weight control as something to help you minimise what might be considered ineffective weight like fat and excessive muscle size. If you can control weight in this way you will often remain functional and continue to improve. You have to remember though that managing weight is a balancing act between diet and activity levels.
A key here is often to get professional nutritionist advice from someone who can test your body mass index, not through a formula of height and weight charts as this is very vague. Instead use more robust measures like multiple fat calliper measure, or DEXA x-ray or underwater weighing. This way you will get a much more accurate idea as to you body fat percentage. You can then work towards a % of body fat that is still healthy for you but better for your climbing.
However managing this with diet alone is tricky and can even be dangerous as if you decrease your calorific intake and maintain training level you will lose weight, but over an extended period can result in overtraining type syndromes, in particular, what is now defined as Relative Energy Deficiency in Sport (REDS). This can lead to systemic health issues, as a result of not providing your body with enough energy for an extended. REDS essentially turns into a chronic fatigue type situation where you will need professional health care assistance to recover even to your previous fitness levels.