A question concerned to the participles

The traveller, being weary, sat by the woodside to rest.

My book says the present participle being weary (passive) is used absolutely in the sentence with the noun The traveller. But it’s separated by a comma and the sentence makes sense without the participle. I think the the book is wrong and it’s a particle phrase or adjective phrase and it’s not used absolutely with the noun the traveller. The noun the traveller is attached to the independent clause and being weary is a participle or adjective phrase separated by the commas. Am I wrong?