I'm going to respond just to this specific quote:
To my mind, emergence evokes a slow progressive process, it starts very small and then it grows progressively. So from that angle, I suspect the distinction between the weak and strong kinds to be in fact quantitative rather than qualitative: with time, a lot of weak emergence will grow strong
If we're defining Strong Emergence as when macroscopic objects have Downward Causal Force over their constituent pieces, then what you've said here, I believe, is not the case.
Weak Emergence has no downward causal force. Ever. And if you stick two weakly emergent things together, there's still no downward force. And if you stick 100 weakly emergent things together, there's still no downward force. There's no quantity of weakly emergent things that will change a system from not having downward causation, to having downward causation.
The most tangible example of this is Conway's Game of Life. Weakly emergent things happen in this game. We know it's weakly emergent and not strongly emergent, because we literally have the source code. Gliders are the classic example of weak emergence here.
You can make large scale "machines" in the game that produce gliders.
And you can make larger scale machines that produce machines that produce gliders.
And no matter how many gliders there are, and how many machines making gliders there are, and how many machines there are making machines, we know for a fact that everything that happens in the game is weakly emergent, because we have the source code. Any time someone wants to say "but wait, what about THIS? Isn't this strongly emergent?", you could check. You could check if any of the pixels were acted on from above, by a 'downward force' from an emergent object, and you would always find in Conway's Game that in fact, no, every pixel obeyed all the pixel-level rules all the time without exception. So there's no downward force, ever, in this game, no matter how much weak emergence you have.
That doesn't mean there's no Strong Emergence in our world, but it does mean that Strong Emergence isn't just the natural consequence of a lot of weak emergence. Weak Emergence + Weak Emergence = more weak emergence.
If there is strong emergence in our world, it is a very different beast from weak emergence. I would say the distinction is valid.