It sunny yesterday, we went out for a picnic.

I have learned that when two subjects are different, either one cannot omitted the example but when they are the same, one can be omitted like the examples.

As he was tired, he got off earlier.
-> Being tired, he got off earlier.

As she was tired, he got off earlier.
-> She being tired, he got off earlier.

And then I was wondering if being also can be omitted although two subjects are different like below.

As she was tired, he got off earlier.
-> She being tired, he got off earlier.
-> She tired, he got off earlier.

As it was sunny yesterday, we went out for a picnic.
-> It being sunny yesterday, we went out for a picnic.
-> It sunny yesterday, we went out for a picnic.


What do you native English speakers think? Thank you so much as usual in advance!