A few PA28s are very nose heavy, so a 17 stone limit might just be a simple rule of thumb that works in some club aeroplanes.
Microlights and gliders usually have a limit - typically somewhere between 86kg and 130kg, depending upon aeroplane. Light aircraft are actually designed to lower seat loads than either but then this is never shown as a limit. That's just a historical anachronism.
Ultimately it is overall weight and especially CG position that really matters. The reality of that is that somebody weighing 19 stone should probably stick to 4 seat aeroplanes like the Cessna 172 or Piper PA28. These cost a little more than a 2 seater, but are perfectly good training aeroplanes.
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