Standing adds power but at a cost of a greater energy requirement. While standing your legs are supporting your weight instead of the bicycle frame. Standing as compared to sitting will add several beats, maybe as many as 10, to your heart rate. The only reason to stand is to go up the hill at a faster rate or to give your legs a rest if you are on a long hill and you can stand up without going anaerobic.

If you cannot make it to the top anyway then standing will hasten having to stop. My buddy is working with me to pace me up hills using my lowest gear while remaining seated. The lower the pace the less watts required and the more likely you are to complete the hill. As a result, I am getting much farther up the hill compared to my old style of going faster and standing. Like you say, if the grade gets too steep and is very long in length, I just have to stop and walk when I run out of wind.

This is a long winded way of saying that the strategy you are already using is the best. Lose weight is the key and hill training but you already know that. If it helps I am in the same situation but only need to lose 20 pounds.