Wire wheel balance problems
Sometimes wire wheels can be a problem to get balanced. Here are a few tips to try and solve it:
Check how the balancing machine locates the wheels. It should locate on the taper on the inside of the wheel centre, with the inner edge of the centre clear of the face of the balancing machine. If this edge is hard up against the balncing machine, the wheel is very unlikely balance as this edge is not necessarily manufactured to run true (after all, it is not where the wheel locates on the car).
Not even new wheels can be balanced this way. Some balance machine operators can't get their heads around this, so you may have to shop elsewhere.
Remove the wheels and look at the splined hubs. Inboard of the spline is a taper, upon which the wheels seats & centres. Check the base of this taper, to see if there is any sign of the wheel splines fretting on it and leaving an impression. If so, it indicates that the taper has worn and this could be causing the wheel to centre inconsistently.
If there is such marking at the base of the taper, check the teeth of the spline - if they are sharp, the hub needs renewing (and if not attended to it will eventually strip just when you need it most - heavy braking when there is the most load on it. I discovered this one the hard way at the tender age of 17, fortunately i didn't hit anything!)
If the spline teeth appear to be in reasonable condition, remove the spline and have a machine shop true up the taper, taking care to have a relief at the base so the splines can't engage there.
Check the wheel where it engages with the taper. If there is a wear ridge, that will be contributing to the balance problem by preventing the wheel from seating consistently. There is no economic alternative that I've discovered other than to replace the wheel, particularly as when a wheel's got to that stage there will be wear in the spines as well.
See if you can try someone else's wheels - just the front will do. If the problem goes, then new wheels are the answer. If the problem remains (and assuming the wheels were OK for balance on the car you borrowed them off) then the problem will be elsewhere.
If the hub taper is badly worn the test is more limited in its value - if the problem goes, yes it's the wheels; but if the problem stays it could also be the taper preventing the wheel from centering properly.