The only issue you should have the word "weight" is regarding losing it.
1. Lose weight.
2. Generate more power.
I'd put losing weight over more power as losing weight is "free speed", it allows you to use less energy for a given speed and in general less body fat = better cooling.
More power is good too.
Less weight and more power really is the only way to go faster on the hills. The other part of the equation revolves around effort/pain/gearing especially on hills where the grade constantly changes more than a few percent in a short distance. Such changes, especially when going from steep (10%+) to fairly shallow (7% and under) can make keeping a steady power output fairly tricky and may require you to change gears more often than you think.
Being heavy and weak on the hills is like being in the circle of doom - not only does it suck going up steep hills, but on variable grades you are never really able to carry that much momentum either. You go slower, you get less cooling effect from the breeze, you get hot which makes it harder to keep the power up, yada yada yada.
If you want to go fast up hills, the last thing you need is more muscle - stay the hell away from the gym unless you have a specific need for exercises in the case of rehab following injury...
The one thing that doesnt need developing is attitude. If you can dig deep enough on the hills to make it feel like you're gonna rip your legs off and set your lungs on fire you'll do fairly well... if you can't then I'd stick to crits and riding down to the shops.