1. Tired, he went to bed earlier.
2. Being tired, he went to bed earlier.
3. As he was tired, he went to bed earlier.
(Are they all grammatical?)
4. As it was sunny, we went on a picnic.
5. It being sunny, we went on a picnic.
6. It sunny, we went on a picnic.
(Are the three all grammatical? Can we delete 'being' as in Sentence 6?)
1 and 2 are very strangely phrased. Use 3.
5 and 6 are strangely phrased. Use 4.