Sounds like a fuel /air mix issue.
If you ride close to sea level - ignore what I’m about to say — if you ride at altitude, it might explain a bit about your predicament.
With TW200’s, the only time they lose “significant” power on hills (assuming the bike is set up correctly), is at altitude. Even at 16 stone, into a head wind, up a hill — you should have been able to get up to 40mph on that 125.
But on that particular night, the high winds indicate a change in barometric pressure — either high pressure or low pressure will have an effect on the air/fuel mix — and if your carb is set up “border line” for your altitude, then this may have been just enough to tip it over the edge.
The fact that the bike was fine the next day tends to confirm this.
Of course, if you’re nearer sea level, then I’m talking out of my arse ……..
Sorry I can’t be of more help — but this forum is set up for TW200’s — not TW125’s. There may be similarities between the two, but anticipating your next question (what should my jet size be at xxxx Ft above sea level) — I have no idea.
If you want some honest advice — at 16 stone in a hilly area — you might want to consider getting the 200 — then we would be able to answer in more detail ……….