Thanks to everyone for advice - all completely spot on. Sunday started off beautifully - this is just after Balerno at around 9:45:
path started off great - really decent surface:
Then we hit the hardcore that IWROTS mentioned on the downhill section:
This is probably the worst surface to cycle on as the covering of loose stones is quite thick. Then we reached the bit that Roibeard mentioned:
and from the other side:
seems like the erosion is caused by the burn occupying where the path used to be.
We managed to cycle all of the rest of path, and there are options at that crossing as it might be possible to cross to the other side, and the burn is quite shallow at that point. Over the grassy sections it's a bit muddy but completely fine on my 28 contintentals. Went on to Penicuik and through Dalkeith to Musselburgh and back to town - horrendous hail later on but at least the wind was behind us at that point!
Thanks again to all for the advice on the path choice.