It's possible that you're losing the bar forward in the bottom of your overhead position because of tight/weak hips/posterior chain, so you just don't have the ability to stay as upright as you should. If that's the case, something like wide stance box squats, or sumo deadlifts may yield some improvement. Just an idea of a myriad of things that could be causing issue..
As for the jerk, I'm going completely off the actual words you used here, but there is no real "catching the weight." When you drive the weight up off your shoulders using your legs, you are more pressing your body under the bar to the locked out position. Kind of the opposite of a push press, where you pop the weight then use your shoulders to push it up the rest of the way. So if you are truly "catching it," that could be leading to some of the instability. The pvc drill Nathan mentioned is good, as is drawing a big + sign on the floor and practicing the footwork.