During my recent flight, the captain announced that he took excess fuel and wanted the weight distribution adjusted in an almost full flight. A passenger was kicked out and the flight attended sent a couple of passengers back and brough one forward. Years back, in a near empty big airliner (only 6 passengers!), we were all asked to go to the back of the plane.

My questions:
1) Is the "weight distribution/balance" arbitarily determined or is there a gadget in the cockpit that indicates plane weight imbalance?
2) In an otherwise full plane carrying over 60 people, does the "re-distribution" of a couple of people make a difference?
3) Has there been any incidence where imbalance played a role in any accident?