stagger
To walk in an unsteady way, almost falling over.
To stagger means to walk or move unsteadily, as if you might fall over at any moment. Someone who's just gotten off a spinning carnival ride might stagger a few steps, wobbling side to side while their sense of balance returns. A hiker who's been climbing all day in intense heat might stagger into camp, exhausted and barely able to walk straight.
The word also means to arrange things so they don't all happen at the same time. A teacher might stagger the due dates for major projects, spacing them out across several weeks instead of making everything due on the same day. A factory might stagger its workers' lunch breaks so that some people are always on the job. Cities often stagger school start times so that buses can pick up high schoolers, then middle schoolers, then elementary students.
When something staggers you (as a verb) or leaves you staggered (as an adjective), it shocks or amazes you so much that you feel almost knocked off balance mentally. You might be staggered by how much your friend's art skills have improved, or staggered by the size of the Grand Canyon when you see it in person. The connection to physical wobbling makes sense: truly surprising news can leave you feeling momentarily unsteady, as if the world has shifted beneath your feet.