To answer I-T-H's question, we have to make the assumption that this aircraft had to reduce its payload. This might have been to carry more fuel (possibly because it had to fly lower) or some fuel could not be used etc., either way let's assume this had to be done. It is entirely reasonable that actual reason is explained to at least the passengers affected. I have had to do this a few times. I'll give a general, Tech-lite explanation to everyone but I'm always willing to give the compete story to anyone who wants it. But continuing, most aircraft fly well when fully loaded. But as the load reduces, the centre of gravity (thus stability and controllability) starts to become an issue. This is because the CofG envelope is not always comprised of completely straight lines and also, as the weight reduces, the envelope becomes smaller. Also there are often kinks in the lines yet the CofG has to remain in the acceptable region thoughout the flight as the CofG shifts with fuel usage. Which is one reason. Another is inoperative hold area and/or abnormal hold masses (cargo) that may have a higher on-load priority than passengers. This restricts your the rest of your payload. Either way you have to loose some and/or shift what you can around the aircraft.
For what it's worth, in performance terms my aircraft can fly full tanks and full payload. But we haven't purchased the increased weight from the manufacturer and at the same time have saved fortune by artificially reducing the maximum (we have purchased) take off weight to reduce airways charges. Most large aircraft, as other posters have pointed out, are unable to do the same.