The best thing you can do for weight loss is look at your diet. If your diet isn't good, then all the bouldering and climbing in the world won't help you to lose weight.
How you go about that is up to you, but as general guidelines:
- Concentrate on whole, nutritionally dense foods (meat, fish, vegetables, fruit and some rice) rather than anything that comes ready made that you just put in the microwave or oven.
- If you're gaining weight, eat a little less until you stop gaining weight. Then cut out a little more and stick with it for a while.
Don't go nuts and drop down to a 1200 calorie diet. You're not a child, you need to eat more than that. Don't do juice fasts, diet teas, Slim Fast shakes, anything like that. Just eat good food.
Exercise wise, find something you enjoy. You've already got bouldering, great, but it's difficult to do that 5 days a week (I know, I've tried it and I've got the injuries to prove it). If you enjoy doing cardio, then carry on doing it, if you don't, then stop.
If you want to do some gym work, I'd use Dan John's template of push, pull, hinge and squat (don't worry about the 5th group as your bouldering should take care of that).
For pushes, look at overhead work, preferably dumbbell or kettlebell for the extra shoulder stability work.
For pulls, concentrate on horizontal pulling, like TRX rows, to strengthen your rhomboids and shoulders (yes, I know you're thinking pull ups here, and you can do them, but they shouldn't be your focus).
For a hinge, a deadlift is a great choice for teaching you full body tension. I also really like kettlebell swings (they're also good for a metabolic hit to help with fat loss).
For a squat, I'd go with single leg work. If you can, do pistol squats, if not, Bulgarian split squats are a good choice.
Throw in some ab work as well, ab wheel roll outs are a great option, though you can also throw in planks if you like (I don't, though purely because I dislike them)
Climb / boulder 2 or 3 times a week, and learn to use your feet more than your arms. Watch how women climb and emulate them. Don't over grip the holds and concentrate on moving smoothly and quietly. Try and make every climb look good, as if you're performing in front of an audience.