Aerith definitly did have a big burden. She was the last of her kind, and thus hunted by the Shin Ra. She could hear the voice if the planet, which definitly has to be a huge weight on one's shoulders. And she had to feel a lot of responsibility for things, whether they were beyond her control or not. What she did, going off to save the world and knowing she may not come back, was very brave. I dont like her at all, but I cant deny that it was brave.

And yeah, the planet's burden was shared by... hmm... Well Barret for sure, who had a lot of responsibilities and burdens himself, Aerith, Red XIII, and Cloud eventually. I suppose Yuffie and Vincent may have cared too, but they had their own agendas, too, that took precidence for them.