Hi Horace,
The 9D was fitted as standard with what Villiers called the Lightweight or L/W carburettor. It is made to fit on a 1" stub. The Mk II markings relate to the various patents and updates and are basically irrelevant. As you have found out they only serve to confuse the owner and anyone else unfamiliar with Villiers little ways.
The last variation fitted to the 9D was the Lightweight 3/1 Special and quite possibly your carb may be one of them. This was a sort of crossover model between the original 9D style and the new 3/4 carb as fitted to the 10D. Many parts are interchangeable between the two.
I recommend very strongly that you get yourself a copy of B E Brownings "The Villiers Engine" published by Pearsons. First published in 1949 and right through until the 1960's you will need an early edition. Browning will explain at length what you have and how to go about sorting it.
I've never had any bother buying new parts but until you know precisely what you have you'll go round in circles.
Finally, Villiers carbs are quite different to tune from the common Amal carb found on British bikes. They are very easy but DIFFERENT. Browning will explain all.
Get back to us once you have a copy of Browning, easily found on the Abebook site
www.abebooks.com Cheers