Depends on the airline and the airport too. I have never once had it weighed though - it is counted as an item sometimes, but never weighed!

Sometimes you can take it all the way to the plane door, sometimes you can take it to the very last waiting lounge, and sometimes they take it at check in (Cairns!).

I contacted air NZ once and they said I'd have to check it in with the luggage, but they actually let me take it to the gate. Then next time I had to check it!
Yes it can be very variable - I tend to use a carrier in the airport and check it in because they can't be relied upon what their policy is (that way it is nicely packed up in a bag less likely to get damaged etc, also I have never had weighed just counted as an item, so managed to sneak a couple of pairs of shoes into the bag :-)), a lot of airports/airlines do have ones you can use - especially transit ones like Abu Dhabi and Singapore, Hong Kong etc if you are doing a long trip and just have an hour or so in one of those airports.