I'm going to assume that your two goals are:
- Improve your performance
- Stay healthy and uninjured
I'm also going to assume that you are healthy and cleared for intense activity.
If you are wanting to increase your anaerobic fitness, you are going to need to do intervals. In this case, I'd recommend all-out intervals; they will place a significant load on your system, and that will cause you to improve. I'd recommend starting with simple sprints twice a week; go out and warm up thoroughly, find a good spot, and then run as hard as you can for about 30 seconds. Recover for 3 minutes, and then repeat. When you can no longer work at the same rate, you're done with the session. Typically, this would be 4-6 efforts; if you hit 6 and still feel okay, you need to up the intensity or add a second set after a 10 minute recovery.
A few keys to having success. First off, if you are running, the sprinting will put a big load on your muscles and you could get overuse. Good shoes and a good running surface will help. Second, intervals work because you can put a large load on your system, and to do so, you must be well-recovered. Make sure you take a few days off between your sessions, and if you can't put out a good effort early in the interval set, abort the session. I would not do intervals more than twice a week, and that may even be too much. Pay attention to your body. I would not do full sets the week of the event, but it's okay to do 1-2.
If you do these right, they will make a significant difference in both your aerobic and anaerobic fitness.
I am a fan of weightlifting in general, but starting a lifting program right before an important skill competition isn't a good idea. You could injure yourself, and even if you don't, you may end up with strangely tired muscles that throw off your timing.
For the weight part, I'd concentrate on good nutrition. Intervals are going to be taking a lot out of you, and if you try to lose weight at the same time, you could go too far.