All the craft I have had experience with are a great deal more stable with a light paddler.

An extreme example is seeing 10 year olds being quite unable to capsize a canoe even when both of then leaned on the gunwale on one side. Their combined weight was less than the righting moment of the canoe at a slight angle.

In a kayak the difference is not usually that extreme, but it is still very noticeable, especially with children who are not only lighter but also shorter so their CofG is lower.

A kayak will tip over if the force which is pushing one side down is greater than the righting moment. That force will be less if the paddler's CofG is closer to the centre of the kayak or if the paddler is lighter.

I just realised as I was typing that the short answer to your question is, yes the lighter paddler feels more stable and the proof is in the stability curves in Ross Leidy's KF.

One example I just looked at has a maximum righting moment of about 6 at 17 degrees with a 150lb paddler.
It has a maximum of about 2.5 at 10 degrees with a 200lb paddler.

That is an enormous difference. Not all kayaks would have the same difference, but a lot would have something similar.