When there’s hills involved there’s two ways to increase your speed to the top. Increase your power, or decrease your weight. Increasing your power will require specific intervals, an increased training load, and a lot of pain. Decreasing your weight involves a whole lot of sacrifice and discipline. Neither are easy. Depending on your current abilities, one may be easier to tackle than the other.
For example, I don’t have a problem generating power. But I’m also 85kg and would likely work to lose 5kg if I wanted to increase my climbing speed. It would take a LOT more work (90% more work for an extra 5% gain) to increase my power with my current training load. My current power to weight ratio at threshold is approximately 5.2. If I were to keep my power the same and loose 5kg I would increase that ratio to 5.6. That would be relatively easy given the alternative. I would need to increase my power by almost 50 watts (a significant figure) in order to get the same results.
If you are already very lean then there’s only one way to go. Increase power output. Assess where you’re at and decide which strategy is more achievable.