Budget airlines at home usually mean no carry-on bag, but budget airlines abroad sometimes allow carry-on bags up to 7 kg. It's one small measure in which, again, North American airlines fail their international counterparts.
There are a few ways to skirt getting a carry-on bag weighed (another article unto itself), but there is one simple trick available to most travelers: check-in online and go straight to the gate.
There are often three layers of airport "checks": the initial check-in counter, the security line, and at the gate. The check-in counter is usually where most the weighing happens. Most line security agents could care less as long as you don't draw attention to yourself (no liquids bigger than 100 ml!), and most gate agents are preoccupied with getting the flight out on time.
Essentially, if you can bypass check-in, it's often a wash as to whether luggage limits will be enforced at the gate.
This was recently tested on a Hong Kong Express flight from Hong Kong (HKG) to Tokyo (NRT) flight. Though we pulled it off with flying colors by checking in through the mobile app, it would have not worked on the first flight from Tokyo (HND) to Hong Kong (HKG). (Online check-in was not available and they totally weighed everything there.)
Clearly, it's all circumstantial. Sometimes it's not possible for a boarding pass to be issued via mobile or online check-in. Or the country you're flying out is known for its draconian adherence to protocol (lookin at chu, Japan). At best, it's worth a Google search.
But do be forewarned, travelers are taking the risk that the bag might actually get weighed. In that case, the consequence is shoving everything into a personal bag or sucking it up and paying those bloated baggage fees at the airport. No risk, no reward.