In reply to Shanes:
Going back about 10-15 years ago, a couple of guys I shared an office with asked me if I would take them climbing, I guess my enthusiasm for it must have been infectious! One of them was as skinny as a rake. The other guy, I don't know how much he weighed, but I would guess it wasn't far off your weight.
They both got really into it, bought all the gear and progressed to leading routes at crags and then in the mountains. The big guy visibly lost quite a bit of weight, and that gave him an extra advantage as his strength to weight ratio improved a lot more dramatically than the skinny guy. Another thing I've noticed of heavier climbers is that they often have better footwork. Skinny folk can often get away with hauling themselves up steep routes despite poor technique. Heavier folk need to develop better technique to keep their weight off their arms as much as possible.
So, don't worry about your weight, just, as others have said, start with slabbier routes, and focus on trying to keep your weight over your feet as much as possible. And I'm sure your instructor will tell you this, but make sure to get your belayer to clip into a sandbag or two so you don't meet each other halfway up the wall!