Clearly you have a problem with the operation of the circuit as the capacitor is taking much longer to charge up than to discharge. We need to ask why that might be? I don't immediately know, but something is clearly wrong there.
What is the supply voltage to the circuit? Also what is the voltage scale on the various traces? Is the output pin voltage changing between 0 and Vcc as you would expect?
The vertical scale on all those pictures is 0.2V/Div, but accounting for the x10 probes I'm using, it's 2V/Div. The trace is slightly too high in those pics. I'm supplying 5V to the circuit and the output pin is going between 0 and 3.6V. The Capacitor charge seems to be going from 1.8V to 3.5V. Since the capacitor is supposed to be charging and discharging through the same resistor, it's odd that the times are different.
I've just tried replacing the resistor in case that was behaving oddly, but there is no change.
I've also just tried replacing the 555 timer (with another 20 year old one). No change.
I've just changed the capacitor to an "identical" ceramic disc capacitor, and realized that the one I was using was 65.1nf which is 38% off from its stated value of 473nf. I've tried several different capacitors, even different types, and the charge time is always much longer than the discharge time. The only change is that the output square wave now seems to go between 0v and 4v rather than 0 and 3.6.
So, in total I've replaced every component in the circuit and checked the wiring many times, yet things are still amiss. I suppose I could rebuild it further up the breadboard, but I'm just clutching at straws.
P.S. I've only just acquired this scope. There is a slight anticlockwise rotation on the trace I think. I'll have to sort that out.