At your weight, little guys are always going to drop you on hills. There's nothing you can do about that, because if you do get faster and start riding with faster groups, the little guys in those groups will be even faster going up hills. It's nothing but power-to-weight ratio, and smaller riders have a huge advantage there.
Get yourself a 12-27 or 11-28 cassette - that will help you not have to mash as much up hills. Or maybe even an 11-32 MTB cassette.
Don't worry too much about specific training for hills - a climb is really nothing more than a hard interval of some sort. Longer ones at or just below your aerobic threshold, shorter ones can be anaerobic (but not too badly anaerobic because you won't recover enough after the climb to avoid getting dropped). Mix things up on your trainer - do some 3-5 minute intervals that are pretty tough, maybe even in a hard gear at low cadence. But DON'T relax afterwards. It does no good to kill yourself on a climb if you're so dead at the top you can't continue, so you have to work on continuing.
Make sure you're getting enough recovery time between hard rides, too.
Most of all, just keep riding. You'll get better.