Yes, you're right there. When you stand your muscles are not only doing the work you need to pedal up hill but to support your standing body.

To stand or sit on hills is a much discussed question for racers, tourists and cyclists in general. There is a lot of good information on line about it.

Sheldon Brown has some interesting things to say about it, which may apply to the OP.

I thought about this thread today. I did a long road ride in very hilly country and at the end of a long 3 mile climb, that averaged about 8%, I spun (seated) at a pretty high rpm until just before the crest of the hill, when I shifted up and stood on the pedals and hammered over the top- no doubt its effective and gives power when and if you need it.

I'll repeat that my suggestion is much like what Sheldon Brown suggests- that for the everyday cyclist this may not always be the preferred method of climbing. certainly on those days when you're "feeling your oats" and want to ride like you're in the TDF by all means stand all you want, but for riding to work every day I would suggest learning to effectively climb in a seated position. If you are having problems with a seated position I would check my seat height and bike fit.