As far as I know, the tyre size, as in diameter, has nothing to do with perceived stability, just that the bigger the circle, the less it's upset by unevenness.
I believe the main reason why a tyre feels wiggly, is down to the contact patch with the road being small, in that particular riding condition.
Most tyres are shaped to increase the contact patch when the bike leans at a particular angle.
Consider the cross section of an ideal tyre for a motorcycle with sidecar, which'll look like a car tyre, ie square. That's because it's always upright.
Now imagine a tyre for a motorcycle that gives the greatest contact patch with the road, when it's leant over at, for example, 20°. Well it'll have a cross section that reminds of a 20° sloping roof.
Also, motorcycle tyres are made of different rubbers. For example in the previous 20° version, that corresponding wide shoulder might be made of soft and grippy rubber while the contact patch when the bike is upright , ie the spine, might be made of harder and longer lasting rubber.
I think the Bridgestone Battlax tyres are something like that.
Think cross section of tyre and therein you'll find it's wiggliness.
Oh, and the fatter the tyre, the wider/ bigger the contact patch and perceived stability (and reluctance to quickly steer round tight bends).