Oh, that is interesting. One thing about standing it is TOTALLY different on road handlebars with your hands on the corners or hoods, palms facing in, than on a flat bar with your palms facing your body. You may find it much easier to learn to climb standing on road style bars.

I can't stand on my MTB but I can stand on my road bike for a long time. That said, I do know a couple of people who can't stand on their road bikes, but I think it's mental, they psyched themselves out of it.

Give yourself time to practice instead of just saying "I can't" - and shift up a couple of gears (harder) - you will learn how.

The weight difference will make some difference. The 10% climbs you should be able to stay seated with a low compact gearing (look at APEX and maybe Shimano has a 30 tooth cog as well) - but those 16%-ers, you will probably need to stand.