Why does Jess think that his life is like a dandelion?

The answer to this question can be found in the final paragraph of chapter seven.

Sometimes it seemed to him that his life was delicate as a dandelion. One little puff from any direction, and it was blown to bits.

The reason that Jess thinks this is because, moments before, his sister May Belle tells him that she knows where he and Leslie sneak off to all of the time. May Belle doesn't exactly know about Terabithia, but she knows the location of the secret area.

Jess, I know where you and Leslie go to hide.

Jess is upset by this news because Terabithia is his special place with Leslie. He feels comfortable around her in ways that he has never felt before, and they share great adventures together. Leslie feels the same way about it as well. Earlier in the chapter she admits that Jess is her only true friend, and Jess feels it is a great honor to be Leslie's "whole" friend.

There in their secret place, his feelings bubbled inside him like a stew on the back of the stove—some sad for her in her lonesomeness, but chunks of happiness, too. To be able to be Leslie's one whole friend in the world as she was his—he couldn't help being satisfied about that.

At that point in the chapter, Jess is feeling an emotional high. Then May Belle announces her discovery, and Jess feels like his euphoric special place with Leslie is being threatened. With one simple announcement, May Belle has completely flipped Jess's emotional state. That's why his life is like a delicate dandelion. In one moment, he is content and completely together, but in the next moment his safe and secure life has been completely blown apart.