So sorry you had a crappy day!
I am 115 lbs and a good climber...but everyone assumes it is because I am light!! I am sure that this fact helps, but I did NOT start out that way. Pound for pound, I am not as strong as a bigger, stronger rider. And while I may billy goat my way up a hill, *everyone* descends faster than me, and THAT, when you have run out of gear and are just coasting, is frustrating.
Lose the weight if it makes you stronger and better, and think about riding with your friend as training! Don't let her drop you! My guy friends drop me on every hill I climb (and they all out weigh me by 50 lbs)....because they are stronger, better, faster riders. But I constantly chase them, so when I ride with a *normal* group of riders (as in not supermen) I easily lead the group up the hill.
I also keep my ipod on while I climb. I know, I know, I know...but being in your zone and spinning up the hill is important. My ipod helps me do that.