Come to think of it, I was asked to weigh my stroller at BNE's check in counters in October last year. I was going F to AKL.
At the time I got surprised by the request given that the suites have the floor space for storage (not overhead bins/risk of injury) and noted that to the staff member. I added that in my 12 years of flying with EK I was asked to weigh my hand luggage only once (which was in SYD '09, F to AKL too but that time the check-in lady was a rude contractor on a really early morning).

The bag weighed about 12KG. I was waived the ok without any fuss.

My assumption is that the staff members who become 'anal' about hand luggage are either misinformed, new to EK/contractors or REALLY bored.