I think that one would have to acknowledge that the seat is "compromised" once the occupant weight exceeds the design figure (probably 215 lb).
Since we've dived into certification aspects - 215 lb has been in FAR 23 for a long while however I'd bet that the PA-28 seat would've been designed to an earlier set - perhaps 170 lb back then. Of course, later certification standards have higher G loads for seats as well. A GA-8 marketing point cf the 206 as I recall. Still, none of that stuff has made its way into any operational limitations of the PA-28 via the POH or an AD.
I agree with Tullamarine - ignorant nonsense. Could be an interesting discussion with the insurance company but I see no point in persisting. I could make up a little placard for that flying school to put in all its aircraft to satisfy their insurance company - "maximum weight permitted on each seat is 77 kg". Maybe a lower weight to reflect the lower design G loads cf the current standards?
Perhaps better to talk to CFIs of some other flying schools.
Of course, the other advice on personal weight is probably good too however I'm an engineer not a medical type so I won't comment on that except: yes, Tullamarine, we could both do with some lightening.
For info, my own aeroplane is self limiting - with a big person in either seat the stick is unable to achieve full travel.