When we flew them LAX-SYD a couple years ago, they did weigh carry-ons at the top of the jetway. They were pretty strict about it and forced people to gate-check anything overweight. It didn't appear that folks were charged for the gate-checked bags, the GA just tagged the bags, set them aside and the passengers boarded. I don't recall noticing any issues with personal items that were reasonably within their guidance - seemed to have been more about weight. Whether all of this is normal for the LAX station, I can't say since that was my one experience on the route and it was two years ago. On several Australian domestic flights I had with Qantas, they never weighed bags though.

If you search on the Qantas forum here, you should find this question has come up before on the forum, and may find some more recent experience. Also, I would bet that this Australian site may have some advice on the matter:

http://www.australianfrequentflyer.com.au/

Personally, I'd just go into it assuming they will weigh to be on the safe side. You could get a travel vest to stash things into as that's an article of clothing you're wearing so it's not weighed. I found a cheap but quite functional one on Amazon that has served me well for years.

It may be worth investing in a lighter-weight carry-on bag as well. Check out the Travel Products forum on here, there are some discussions and recommendations. It will also save you some wear and tear on your shoulders/arms! Plus many non-U.S. airlines have carry-on weight limits, so a lightweight bag will probably serve you well for many future trips.

I don't know if either of you are traveling elsewhere in the region on your trips, but in my experience Air New Zealand is strict with carry-on weight. Departing AKL, our bags were weighed at the check-in counter (where they were tagged to indicate they were OK) but they also weighed them again just before entering the security checkpoint area. They didn't weigh bags at the gate so long as you had the tag on them.