“If the airline has no published weight restrictions for passengers and they are basing their decisions regarding who is ‘too fat to fly’ solely on the personal opinion of whomever happens to be working the boarding gate...”
It’s not the weight. So a weight limit would not make sense. It’s the ability to fit into a single seat with the armrests down. I’d bet that the only people singled out are those who, by observation, can not fit by a WIDE margin.
I rarely fly and have yet to do so since 9/11. What I have previously observed in those few time was a 'Test' box near the counters to see if your carry-on will fit in the overhead bin.
I see the solution as a 'Test' seat mock-up at the ticket counters to see if you'll fit before check in. The seat would also have to have side binders to be sure that one cannot overflow the armrest.