I was into climbing years ago. Just top-roping... I didn't get into lead or multi-pitch because I didn't have the budget to travel and locally, there just wasn't anything that justified spending the money on a bunch of camming devices and such.
Anyway... there was a great climbing site nearby with some awesome bouldering routes. I'd go there w/ a group of friends and we'd climb all day... trying different approaches and different routes. When the summer ended, I was lean as hell and I had built strength where I needed it.
My point is that if you want to be better at something... do it more. This is especially true of climbing because you will be using your muscles, pushing and pulling in weird, contorted positions and angles that you just can't replicate in the gym.
Take grip strength for instance. Grip strength in the gym doesn't translate to grip and tendon strength when you're wedging just one or 2 fingers into a crevice or trying to pull on a rock formation the size of a pencil eraser.
Sure, the gym can help... but the real gains will come from actual climbing.
Also, loosing the abdominal fat is hugely beneficial... but not just for weight. It also helps your dynamics when climbing. There will be certain instances where to get the leverage or balance you need to pull a certain move, you will have to flatten your body into the cliff-face as tightly as possible. In this situation, the closer you can become "one with the cliff"... or better stated, the less you have sticking out from the clifff... the more stability you have and the more likely you will succeed in the move.
Check out anything by Chris Sharma....