All referenda in the UK are advisory, and non-binding. Parliament doesn't technically have to abide by their decisions at all, but it would be damaging politically not to do so.

Brexit passed with 51.89% of the vote, so apparently.

Well that seems quite silly. You'd think you'd want a majority for a big, hard to reverse decision like that, otherwise it will oscillate back and forth.

Well not really. You do want to bias for dissolving a union.

If half the population is against it, it doesn’t matter if it’s 51% or 49%, it’s unpopular enough that it is tearing your nation in two.

Imagine the US civil war came down to a vote: “Sorry, 50.1% are in favor of slavery so we’re just going to keep practicing it in all of America”. Would the 49.9% be happy to live within that union? How about vice versa? The division is too deep.

If each 50% happens to be more or less perfectly geographically distributed, sure, but if not then you've just recreated the same problem twice (now something approaching 50% of each new division wants to immediately undo what you've just done).