How does a bag look heavy?
Did they have scales or was this just based on visual observation / pax confessions?
I'd go with visual, thrown in with a bit of along the lines of the same stereotyping that gets some people a second or third look by security screening or border control staff.
Maybe they won't weigh 300 pax worth of cabin baggage, but that could well be because doing so is exhausting - boarding would likely need to start 60 min before departure - and frustrating, i.e. when you tell a pax that they are refused until their bag comes down in weight or is checked in, you create a problem that will waste time and delay boarding. Add on that that everyone thinks elites should be thrown a bone when it comes to the rules; the optics of that to others lining up or being told to repack, reconfigure or get off.
That's why it's rare, unless you're a LCC.
Some airports were putting cabin baggage weigh-ins at security screening. That of course relied on usually airport contract or security company staff knowing all the various baggage allowances, including rules like for medical equipment, infant allowances, etc.
Of course, we're just talking about weight. Critically there is also size and pieces.
Here's a thought: would you penalise a passenger for going shopping at the airport, even if those items are rather large and heavy? If you do, that might discourage passengers from shopping (e.g. including duty free), which the airport won't like because that's their moolah.
