How do I weigh a kitchen island to determine what size castors to get?
When buying castors, they're generally marketed as a set that can carry a total load.
ie a set of 4 '200 lb' castors are meant for an object that weighs under 200 lbs.

I'd simplify your problem by estimating then doubling that. If an average person can lift 50 lbs, is the kitchen island something 2 people can lift? Get a set of 200 lb castors.

Would it take 4 people? Get 400 lb castors.

The difference in cost of castors is small enough that I might just get 1000 lb castors and call it a day.