In Act 2 Scene two, she says she wishes he were a bird on a string so that she could have him gone no farther than "a wanton's bird, that lets it hop a little from his hand like a poor prisoner...and with silken thread plucks it back again." She wishes to let him fly, but not far--when he gets too far, she wants to be able to pull a silken thread to draw him back.
Romeo is willing enough to be her "bird", telling her " I would I were that bird". Yet Juliet withdraws her request, saying that she fears she would kill it with too much cherishing. It is an apt metaphor. Children's birds, being tied to their wrist and pulled down at will (sort of like a helium baloon), didn't live very long and, as it turns out, neither will Romeo. Although it is not the cherishing that kills him, exactly.