It could be based on speed rather than mass. Above 5-10 mph or so, you turn a motorcycle with pretty much total countersteering, forcefully pushing forward on the inside hand grip to get the motorcycle to lean over. The faster you're going, the further you need to lean the motorcycle.

That makes sense too.

The geometry is set up to be stable at a higher speed. Even then some sports bikes require a steering dampener to prevent "speed wobbles" (which, yes, are an actual thing and are much worse at 260kph than at 30kph on your BMX when you're a kid.)

Is "speed wobble" anything like the Jeep "death wobble" (actually can happen on any 4wd vehicle, but Jeeps seem to have the problem more as steering and suspension components wear)?

I hadn't heard of the "death wobble" but it sounds like the same thing. Basically your suspension geometry is set up to be dynamically stable over a wide range of speeds, but if you go outside that range it's possible for oscillations to build up. Example on a bike: https://youtu.be/SAnjjHKclZs