I don't know the format but I like the image of the bits, looks like a heavy rainstorm 
It is not clear how you got these samples, how your code looks like, so it is impossible to make an interpretation from here.
that said:
- you identified a repeating [no info?] pattern, so you should be able to strip that
- you need to add timestamps to individual samples, makes analyzing better possible
- I think your samples are not the bits, the data looks a bit oversampled. I think that ~3 zero bits = LOW and ~3 one bits = HIGH.
Q: please post the link to the datasheet of the weatherstation (or any other info you have)
Q: please post your code