In season 6 episode 10 we saw:
Jon Snow was proclaimed King in the North and everyone present chanted "King in the North" for Jon including the Lords and Knights of the Vale.
This is unusual because:
- The Vale has always been a distinct Kingdom in Westeros, ruled by House Arryn for centuries.
- In the past, the Vale and the North were bitter enemies and fought several wars over the islands of Three Sisters for centuries.
- Valemen are mostly Andal (with a few exceptions like the Royces, Redforts etc.) while Northmen are mostly First Men (with a few exceptions like the Manderlys)
- Valemen follow the Faith of the Seven while Northmen follow the Old Gods.
- The Vale's Lord Arryn is cousin of Lady Sansa Stark but he is not related to Jon Snow at all.
- The Vale has never been ruled by any Northern House while North has never been ruled by a Valeman.
So given all this, the Vale is a distinct region with ethnic, religious, social and historical differences with the North. They do not have any reason to support Jon Snow's bid for sovereignty.
Petyr Baelish may have brought the Lords of the Vale with him in hopes of marrying Sansa and seating her on Throne of Kings of Winter but that hope has gone awry given that Sansa has spurned Baelish's proposal.
Some people may point out that the Riverlords previously did so as well when Robb was proclaimed King in the North, but the Riverlands have never been independent for a long time. Before Aegon the Conqueror came, they were ruled by the Ironborn. The Royal Houses of the Riverlands are extinct, unlike the Vale where House Arryn still rules.
So why would the Lords of the Vale accept the rule of a Stark bastard instead of supporting independence of the Vale in alliance with the North?
Or in case that it is my misunderstanding the Valemen took Jon for their King (it is possible that they may have been just acknowledging Jon's sovereignty on North), is there any evidence that they did not proclaim Jon as their King as well?
EDIT: It has been pointed out that Baelish said he had declared for House Stark so Valemen Aristocrats were right to join the chant. What is not pointed out is that Baelish explicitly told Sansa that she was the future of House Stark. Jon is not a legitimate member of House Stark and was still a bastard. Northmen may have some sentiments of Stark loyalty and revenge for Red Wedding playing for them but that is nothing to Aristocracy of Vale. Why should they suffer a bastard of a Northman to be hailed as King? Why should they kneel before a bastard when they can kneel before their own trueborn Lord who comes from line of Artys Arryn, the Falcon Knight.