Losing weight always helps climbing, unless it means you also sacrifice power. It's all about the sustained watts per kilograms.

I use to hate climbing out of the saddle as I'd get tired in less than ten seconds. I think I was just doing it wrong. When climbing out of the saddle make sure you shift up a gear or two so you have a lower cadence (around 70?). From there stand and lean over the bars. When you get back to your seated position make sure to shift back down to get back to a comfortable cadence.

That's just the technique though. If you really want to get better at it, do intervals so that you're used to putting out more power for extended periods.