Weight is probably the smallest contributing factor to pulling the hill. If your main reason for getting a new bike is to commute with on tarmac, I would totally stay away from suspension. It will just make climbing the hill harder, defeating the purpose of getting a new bike. If your current frame is too small, get rid of it. It sounds like you just need a bigger frame without suspension, and maybe another lower gear. The FX series bikes sound great. If at all possible, I would try to take some other bikes for test rides for comparison before making the final decision. Maybe if you take a trip to another town stop at their shops or something. Even if you don't get their bikes, it'll help you get a better idea of what you're looking for.

As for the standing while pedalling issue, why do you lose your balance? Can you stand and pedal with another bike? Can you do it on your bike without the extra weight on it?