Is passenger weight distribution important on a commercial flight?
On the EMB-145 the passenger cabin was split into 5 zones and we were given passenger totals in each zone from the flight attendant prior to leaving the gate.  If balance is off (this happened quite rarely for us) you would tell the flight attendant "I need 2 passengers from zone 5 moved to zone 1" or "I need a passenger from zone 3 moved to zone 2" or some other similar instruction.  The flight attendant would solicit volunteers and if no one did, they would instruct someone to move.  The move was only for takeoff and once airborne they could go back to their normal seat.

After moving passengers we would re-calculate the weight and balance to verify we were in the envelope and set takeoff trim.

Similar methods are used in larger airplanes with the cabin split into zones.

The only time we would use ballast is when we had a full cabin and not enough bags in the cargo (not common).  In those cases we would ask ops for ballast and they would put something in the cargo.  They would try to make it useful if an outstation needed something else they would just load 50 lb bags of sand.