There are only a few numbers under 500, so I consider that noise
There are a few very large values, => ignored too.
It looks like the basic bit width is around 512 micros()
I interpret the values between 512-700 as the times between 2 bytes. When the weather station has clocked out one byte they wait a little longer than one bit before sending the next byte.
Now the step is to write a sketch that accepts 8 bits clocked out to be samples every 512 micros() and that sketch needs to synchronize on the first LOW.
Rob