The cable is 62,000 miles long. The atmosphere goes up maybe 100 miles (0.16%) of it, and meaningful wind only goes up about ten miles (0.016%). The pressure doesn't even register.

That said, I've got to imagine that bottom .1% of the cable will be made differently to counteract all the water and oxygen around it.

But you can't rule out the possibility of a storm crossing the cable.

Compared to the rest of the tension and abuse on the cable? I think you pretty much can.

Lightning might be interesting but wind is no big deal.

I wonder about the rotational speed changes of the payload mass more than the wind. The counterweight will tend to speed up and slow down as the mass of the payload is accelerated and decelerated (during climbs and descents respectively), but I keep hearing that the counterweight is just a mass.

If you think the counterweight will move down when you thrust a mass up, you have a misconception. The tether will be consistently under tension, so unless the acceleration mA is sufficient to surpass MV^2/R, that won't happen.

These are all great questions but why do we have to imagine the answers, can we just simulate the damn thing and settle if it would work or not? It seems almost all parameters are known for such simulation except the material used for cable is not invented yet.