It is now difficult to start, the pull handle feels like its going to fall of at the next pull every time.
Ok....it did fall off at the next pull
2 metal 'weights' plastic riveted on....or were....no chance of a start now
From memory the Suffolk Punch shares the same engine as the Suffolk Colt so opens up another spares avenue. The recoil starter is held on by three nuts and once removed exposes the metal parts that fling out to engage the starter and then spring back. The spring, cord etc is straightforward so I assume the fling out bits have come adrift. If you can't find a replacement and you're feeling brave, you can knock up a bracket to fit the flywheel slots and start it with a drill. You just need to be very quick at removing the socket once it starts.
The carb is straightforward as you've probably already found out but both of these models were prone to fuel tank tap leaking. If you know someone in a machine shop, both the footplate (cutting edge) and blade can be sorted. We used to remove the blade (chain driven) and stick it in a lathe with a running centre. You could always tell when one of us was doing it by the ping ping ping as the cutter touched the cylinder blade.