The Single Speed Shopper of Death™ and other shopping bike tales

It is quite heavy through. It did have a massive ladys saddle (replace by a probably equally heavy Brooks). I'm not going to go all WW but I would like to loose some of the wieght.

First things to my mind would be:

Headset (it's adjustable with a steel QR right now)
Seatpost (steel)
Seat collar (also adjustable)

The best upgrade for any steel-wheeled bike is aluminium wheels/rims - IIRC Kingpins have 440mm (500a) rims, so BMX 406 rims might fit without changing the brakes, although you would need new tyres. You can go for long-reach brakes if the stock Weinmann units don't reach. New rims/wheels will save a large amount of weight, aid acceleration (reduction in rotating mass), as well as providing better braking especially in the wet.

I wouldn't worry about the seatpost collar or headset unless you're going weight-weenie - these are steel on a lot of bikes anyway. I'm not sure what happens in terms of folding ability when you replace the stem...

After the wheels, the heaviest things are the cranks (you can swap in a cotterless square-taper axle (or whole new BB, as the Kingpin has standard threading) and modern square-taper aluminium cranks), the seatpost, the saddle and the handlebars. You could also remove the mudguard and chainguard but they're not particularly heavy and rather useful.