yes but a proxy war also weakens the us and given that the us had known interest in canada
Unless the British are willing to invade the US, it is a losing proposition. It might stall the US for a few years, But it should be obvious to the British that the end result (barrung an actual British invasion) will be a US victory that creates a stronger US army and Great Lakes navy. Look at recent British history in North America. The American colonists learn a lot from the French and Indian War, and that knowledge was turned against the British.
The Americans weakness at this time is lack of federal forces due to the several states keeping their own minor forces. A proxy war with the British in the NWT will reverse this.
There net result is a larger, not reduced, threat to Canada.
at the time weakening the us is in the brits best interest.
I think I'm going to need some proof that weaking the US is more important than, say, developing and expending her position in India.
A weakened US is likely to look to Britain's rivals for support. Is that in Britain's best interest?
its also worth pointing out that countrys frequently do nonsensical things in order to spite there rivals.
You know what the British historically did far more often than spite rivals? Protect their trading interests. British trade with the US is worth far to much to risk over land they can't exploit. Expending British interests in other areas such as India offers far more potential. I suspect you far over estimate the British elites desire to spite the US.