Just read the synopsis on Wikipedia, and actually I'm not so offended any more by the notion of gravity that only works on matter from one world.
But reading the synopsis didn't make me think the film was any better: apparently the main character goes to Up (a name which I still have severe problems with) by packing his pockets with matter from Up. That's not a crazy idea: what's crazy is that in order to do this, he'd have to pack his pockets with enough matter to make up more than his own mass. I don't see any reasonable way for him to inconspicuously carry over 200 lbs worth of matter in his pockets.
Also, the fact that the matter burns after a while is a little bit strange...considering the two worlds clearly exchange air.
In the trailer he has a belt on which he straps what looks like large pieces of lead or something like that.
But that's the problem with the movie. I could be OK with twin planets. I could even accept that for some weird reason, things and people are only affected by the gravity of their "native" planet. The problem is that after watching the trailer, it seems that a lot of the plot elements of the movie revolve around this weird gravity stuff, which would require the spectator to frequently think about it, how it works, etc. in order to figure out what the characters are doing and why.
Which would be fine, if it made any sense at all. But it doesn't, and the movie keeps calling attention to that. This is like shooting yourself in the foot and then pouring vinegar on the wound every 5 minutes.