Answer:
From line 11 of ''Sympathy'' - 'When he fain would be on the bough a-swing' , I think the word 'bough' could mean something to rest on more like a stick or branch since the poem talks about a bird.
Explanation: Reading from the beginning of the poem, we see that the poem talks about a bird. From line 10 before line 11 where the word 'bough' is mentioned:
''10. For he must fly back to his perch and cling''
11. When he fain would be on the bough a-swing;
In my thoughts if a bird flies back to his perch and clings, perch is more like a resting place on a tree for birds and it clings, it is definitely holding on to something and since it's on the tree it would be majorly a branch on the tree. so this then gives an idea of what line 11 talks about. Furthermore, when an animal is a-swing like a bird or a monkey, it's from/on a branch usually strong enough to support it.
According to Merriam-webster dictionary, 'bough' means a branch of a tree, especially a main branch. It is pronounced /baʊ/
