My club is (honestly) rigorous about max weight. Two PA38's - one empties at 1234lbs, the other at 1170lbs. The latter is operated like the former - 16 imp.gals max. Given 11.5st instructors (2 short-ar$!s, one beanpole and a female), means that the former goes out at close to MTOW normally, the latter with a significant margin. The latter is the machine of choice for Skills Tests. We simply don't muck about with this - the owners of the aircraft, the instructors, the Club. We're as one on this topic.
Operating beyond MTOW is not just about performance and handling. The designer will base airframe life on a usage spectrum; MTOW will be part of this spectrum. Going outside of MTOW may therefore have implications for airframe life.