You can't makes broad, sweeping generalizations like "UK/US type self checkout." It varies so much.

I live in the US and the only place I ever go to where they weigh the items you scanned is Costco. Everywhere else I go (my local Walmart, Target, two local grocery stores, CVS) the self checkout is mostly based on trust with one employee somewhat monitoring some machines. No random sampling.

The only issue I ever run into with the self checkouts is double scanning the product. You do need employee to void items.